Important term & concept

Light. Light is a form of energy. It brings the sensation of sight. It is a form of electromagnetic radiation.
It also provides us means of communication (fibre-optics).

Light wave. Light wave travels with a speed of 3×10⁸ ms⁻¹  in free space. Its speed depends on the medium. For example, in water or glass, its speed is considerably less than the speed in air or space. It is transverse in nature and does not require any medium to propagate.

Ray and Beam. Light travels in a straight line –Rectilinear propagation. The straight line indicating the path of the light (arrow-direction) is called a ray. A bundle of rays originating from the same source of light in a particular direction is called a beam of light.

a) Parallel beam. When the rays which constitute the bean are parallel to one –another, then it is called a parallel bean of light
b) Convergent beam. When the rays are actually meet or appear to meet at a point, then the bean containing such rays are called convergent rays.
c) Divergent beam. When the rays are actually diverge or appear to diverge from a point, then bean containing such rays are called divergent bean and rays are called divergent rays.

Reflection. When light falls on a surface and gets back into the same medium, it is called reflection. A highly polished surface or mirror reflects the light

Incident ray. The ray of light which falls on the reflecting surface is called incident ray.
Reflected ray. The ray of light which gets reflected back in the same medium from the reflecting surface is called reflected ray.
Normal. A line segment perpendicular to the plane of the reflecting or reflecting surface at the point of incidence is called normal.
Angle of Incidence. The angle between the incident ray and the normal at the point of incidence is called angle of incidence.
Angle of reflection. The angle between the reflected ray and the normal at the point of reflection is called angle of reflection.

Laws of reflection.
i. The incident ray, the reflected ray and the normal at the point of incidence, all lies in the same plane.
ii. The angle of incidence is equal to angle of reflection. i.e., ∠I =∠r.
11.

Plane mirror. A plane mirror always forms an erect, virtual, size to size image, at the same distance as the object is, laterally inverted, but at the back of the mirror.
• Its magnification is +1.
• It forms a perverted image i.e., left-right interchange.
• When a plane mirror is turned by an angle θ, the reflected ray will turn by an angle of 2θ.
• To see the full size image of a person, he needs a mirror of length half of his height.
• The radius of curvature of a plane mirror is infinity. Its focal length is therefore, infinity.

Spherical mirror. Spherical mirror is a part of hollow sphere with one side having silver/mercury coating, further coated with point to protect it from damage. According to the position of silvered surface, spherical mirror are of two type:
a) Concave mirror: Silvered at outer surface, so that reflection takes place from inner surface i.e., at the bent-in or concave surface. Example: Inner surface of shining spoon behaves as a concave mirror.

b) Convex mirror. Silver at inner surface, so that reflection takes place from outer (convex) surface i.e., at bulging out surface. Example: The outer surface of shining spoon behaves as a convex mirror.

IPORTANT TERM ASSOICATED WITH MIRROR
Aperture. The width of the reflecting surface from which reflection takes place is called aperture (AB)

Pole. The central point of the reflecting surface spherical surface is called pole (P). It lies on the surface of the mirror.

Centre of curvature. The centre of the hollow sphere of which, the spherical mirror is a part, is called centre of curvature(C).

Radius of Curvature. The separation between the pole and the centre of curvature or the radius of the hollow sphere, of which the mirror is a part , is called radius of curvature(R), i.e., PC= R

Principal axis. The straight line joining the pole and the centre of curvature is called principal axis.

Focus. The point F on the principal axis, where a beam of light parallel to the principal axis actually meet after reflection (in case of concave mirror) or appear to come from (in case of convex mirror) is

Focal Length. The length or separation between the pole and the focus is called focal length i.e., PF=ƒ

Relation between Radius of Curvature and Focal Length. It is twice of the focal length, R=2ƒ

In order or drew diagrams, we need to use any two of the following rules.
i. A ray of light parallel to the principal axis will pass through the principal focus of a concave mirror or appear to diverge or appear to come from the principal focus of a convex mirror after reflection.

ii. A ray of light parallel passing through the principal focus of a concave mirror or going towards the principal focus of a convex mirror, will energy parallel to the principal axis after reflection from the mirror.

iii. A ray of light passing through the centre of curvature of a concave mirror or move towards the centre of curvature of convex mirror, retraces its path after reflection.

iv. A ray of light incident obliquely at the pole of the concave mirror or convex mirror gets reflected at the same angle on the other side of principal axis; thereby follow the laws of reflection.

New Cartesian Sign Conventions. The set of rules, to use ‘+’ or ‘−‘ signs with the values while doing any problem in optics, is called sign convention. They are –
i. The object is always placed to the left of the mirror, so that the incident light moves left to right.
ii. All distances are to be measured from the pole of the mirror i.e., from origin of coordinate axis.
iii. The distances measured in the direction of the incident light will be taken as ‘+ve’ (along positive X- axis) while those measured to the left of the origin (along negative X-axis) will be taken as ‘−ve’.
iv. All measurements of heights above the principal axis (along Y-axis) are to be taken as ‘+ve’ and below it (along negative Y-axis) are taken as ‘−ve’.

Depending on the position of the object. Image formed by a spherical mirror varies in nature. Image formed by concave and convex mirror and its nature, for various positions of object is listed in the following table:

Remember:
• Concave mirror forms virtual, erect and enlarged image only when object is in between the pole focus.
• Convex mirror always forms a virtual image irrespective of the position of the object.

Rules for formation of image by concave mirror;
Rays , parallel to principal axis get reflected back through focus
Rays passing through the focus will emerge parallel to the principal axis after reflection.
Rays from the centre of curvature get reflected back along its own path.

Rules of Image formation by convex mirror:
Rays parallel to principal axis get reflected and appear to come from the principal focus.
Rays going towards the principal focus ,will emerge parallel to principal axis after reflection
Rays from the centre of curvature get reflected back along its own path.

Concave Mirror can be used As shaving mirror.
i. As a reflector to concentrate light.
ii. In a reflecting type astronomical telescope.
iii. In search light, headlight of automobiles, etc.
iv. In ophthalmoscope, parabolic (concave) mirrors are used to examine eye, nose, throat and ear of a parson.
v. Used by a dentist to observe cavities in the teeth.

Convex Mirror can be used
i. As rear-view mirror in automobiles because it
a) Gives a wider field of view as the mirror is curved outward.
b) Produces erect and diminished image of the traffic behind the driver of the vehicle.
ii. As a device to check theft in shops.
iii. To bring view of comers which are not directly accessible?
iv. To lighted a large area.

Mirror Formula. 1/𝑓 =1/ 𝑣 + 1/𝑢 where 𝑓,v and u are tha focal length, image distance and object distance. This formula is valid for concave and convex mirror in all situations for various positions of this object.

Magnification (m ). It is defined as the ratio of the size of the image (h₁ ) to the size of the object (h_a ).

Magnification m is –ve for real and inverted images and +ve for virtual and erect images. So, magnification is always +ve for a convex mirror, while it depends on position of object in concave mirror. If,
i. M < 1, image is diminished.
ii. M > 1, image is enlarged.
iii. M = 1, image is of same size as that of object.

Refraction. When light enters from one medium into another obliquely, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light. Light bends on undergoing refraction. When light enters from rarer medium into a denser medium, the speed of light decreases. So, it will towards the normal as shown in figure (i). Similarly, when light gets into rarer medium from a denser medium, the speed of light increases. So, it will bend away from the normal as shown in figure (ii). For rarer medium to denser medium, ∠I > ∠r
For denser medium to rarer medium, ∠I < ∠r

Optical density : It is the ability of the medium to refract light rays .when the light rays travel from optically
Rarer to denser medium it slows down ; bends towards normal ; ∠I > ∠r
Denser to Rare medium it speed up ; Bend away from the normal ; ∠I < ∠r

Angle of Incidence. The angle between the normal (at the point of incidence) and the incidence ray is called angle of incidence (i).

Angle of Refraction. The angle between the normal (at the point of incidence) and the refracted ray is called the angle of refraction (r).

Laws of refraction.
i. The incident ray, the normal and the refracted ray, at the point of incidence, all lie in the same plane.
ii. The ratio of the ‘sine ‘ of the angle of incidence (i) to the ‘sine’ of the angle of refraction (R) is a constant, for the light of a given colour and the given pair of media. This law is also known as Snell’s law of refraction.

Refractive Index. The constant of the ratio sin/sin  i/r is called refractive index (n) of the second medium with respect to first and given by n₂₁ . If light travels from a rarer medium (1) to denser medium (2), then the refractive index of the denser medium with respect to the rarer medium is given by,

Reversibility of Light. The path of ray light after reflection or refraction when reversed, will retrace its

Relation between Refractive Index and Speed of Light. The refraction index of the medium depends upon the speed of light in two media as the light propagates with different speed in different media. If the light is travelling from medium 1 into medium 2, then the refractive index of medium 2 with respect to medium 1 (n₂₁) is equal to the ratio of the speed of light in medium 1 to the speed of light in medium 2.

The refractive index of diamond is 2.42; it means the speed of light in diamond is 1/2.42 times the speed of light in air or vacuum.

Absolute Refractive Index. The refractive index of medium 2 with respect to vacuum or air is considered to be its absolute refractive index. It is represented by n₂. It is also equal to the speed of light in vacuum to the speed of light in the medium.

Refraction though Rectangular Glass Slab with Parallel Faces. The refraction takes place at both air-glass interface and glass-air interface have the following characteristics:
i. When a light ray travels from air to glass, the angle of incidence is greater than angle of refraction (∠r < ∠i). So, ray bends towards the normal.

ii. When a light ray travels from glass to air, the angle of refraction (also called angle of emergence in case of glass slab) is greater than the angle of incidence of glass-air interface, (∠e > ∠r) ray of light bends away from the normal.
iii. If the angle of incidence is zero, i.e., incident ray is normal to the interface, the ray of light continues to travel in the same direction after refraction.
iv. The angle of emergence and angle of incidence will always be equal.
v. Emergent ray is parallel to the incident ray along with original direction but it will be laterally displaced i.e., light ray is shifted sideward slightly.
vi. For the same angle of incidence, lateral displacement is proportional to the thickness of the glassslab.
vii. For the same thickness of glass-slab, the lateral displacement is proportional to the angle of incidence.

Relative Refractive Index of Two and more than two media. Let us see how the Snell’s law is applied for combination of three media. Let PQRS be the path of a ray of light passing successively through air, water, glass and emergent in air again.

Therefore, refractive index of water with respect to glass is equal to the ratio of the absolute refractive index of water to the absolute refractive index of glass.

Apparent position of Object. Due to refraction, the water tank appears shallow. The apparent depth of the tank is equal to 1/n times the original depth.
If ‘O’ is real object position then T is apparent position.
Refractive index of the liquid w.r.t. air is,

This is another application of Snell’s law.

Effects of Refraction of Light.
a) The bottom of a tank or pond, filled with water appears to be raised.
b) A coin placed at the bottom of glass tumbler, appears to be raised.
c) When a straight rod or a spoon or a pencil, partly immersed in water, viewed from the sides, they appear to be broken/bent.
d) The part of the rod/pencil/spoon inside water also appears thick, if viewed from the sides.
e) When lemon kept in water in a bowl/glass tumbler/jar viewed from side, it appears larger than their actual size.
f) An ink mark or a line drawn on a piece of paper appears to be raised when viewed by keeping a glass slab/glass beaker over it.

Lens. When two spherical or plane refracting surfaces are joined together, they from a lens. The lens, we normally use are convex or concave. A lens, therefore, defined as a transparent portion covered by two spherical or one spherical and one plane surface. The lenses are shown below:

Type of lens:
a) Double convex lens: If both the refracting of the lens is convex, then the lens is said to be double convex lens or simply convex lens. It is thicker at middle and thinner at the edges.
b) Double concave lens: If both the refracting surfaces of the lens are concave, then the lens is said to be double concave lens or simply concave lens. It is thinner at the middle and thicker at the edges.

In order to draw ray diagrams in lenses, we need to use any two of the following rules.
i. A ray of light from the object parallel to the principal axis, will pass through the principal focus (second) after refraction in a convex lens. In concave lens, it appears to diverge from the principal focus ‘ F₁‘ on the same side of the incident ray.

ii. A ray of light passing through the principal focus (first) will emerge parallel to the principal axis in case of convex lens or appear to meet at principal focus of concave lens after refraction and will also emerge parallel to the principal axis.

iii. Any ray of light passing through the optical centre of the lens will emerge without any deviation after refraction through both the lenses.

IMPORTANT TERM ASSOCIATED WITH LENS
a) Optical centre: The centre point ‘O’ on the principal axis, of the lens, through which incident ray of light passes undeviated with negligible lateral displacement is called optical centre of the lens.
b) Centre of curvature: The centre of the sphere, whose part is a spherical surface of the lens is called centre of curvature. Since, the lens have two spherical surfaces so two different centre of curvatures c₁and c₂ lie on either side of the surface.
c) Radius of curvature: the radius of the sphere from which the spherical surface of lens is made, is called radius of curvature of lens. So, each surface of lens having separate radii of curvature R₁and R₂ respectively.
d) Principal axis of lens: A line c₁ c₂ joining the centre of curvatures c1and c2 of the two spherical surfaces is the principal axis of the lens.

For the refraction by spherical lens, we assume
i. Lens is to be a thin lens having small thickness.
ii. Aperture of the thin lens is small, much less than its radius of curvature.

e) Principal focus:
i. Convex lens: When a parallel beam of light is incident on one of the spherical surface of a convex lens, the rays after refraction through it, meet at a fixed point on the principal axis, this point is called the principal focus of the convex lens.
Same effect can also be obtained from the other surface also. So, the convex lens has two focuses F₁and F₂ one on each side of the lens.

ii. Concave lens: When a parallel beam of light is incident on either of the spherical surface of a concave lens, after refraction through it, they appear to come from a fixed point on the principal axis. This point is called the principal focus of a concave lens

iii. Focal length: the distance of the principal focus from the optical centre of the spherical lens is called the focal length ‘ƒ’ of the lens.
If the lens (both spherical surface) is surrounded by the same medium having equal refractive indices and equal radius of curvature, then the two principal focal length of the lens will be equal, i.e., OF₁=OF₂ =ƒ

The focal length of the lens depends upon the following factors:
a) Radius of curvature of bath the refracting surfaces and
b) Refractive index of the material of the lens.

To find Focal Length. To get rough focal length of a convex lens, focus a distant object to a screen, using the convex lens. The distance between the lens and the screen is called focal length.

Sign Conventions. The same rules of sign convention as that of the mirror used for lenses. The focal length of convex lens is taken as +ve and the focal length of a concave lens are taken as –ve.

The table below gives the position. Nature and ray diagram for various object, in convex and concave lens.

Remember:
• Convex lens forms erect image only when the object is in between the optical centre and the focus, but it is virtual.
• Concave lens always forms a virtual, erect and smaller image whatever be the position of object.

Lens formula. If u,v and ƒ  are the object distance, image distance and focal length respectively, then,1/ 𝑓 =1/ 𝑣 +1/ 𝑢.
Magnification of a Lens.

Magnification of real and inverted image is taken as −ve and for virtual and erect images, it is taken as +ve.
Magnification produced by convex lens can be less than 1, equal to 1 or more than 1 depends upon size of image. On the other hand, magnification produced by a concave lens is always less than 1.

Power of a Lens. The ability of a lens of converge of diverge the rays of light, is called power (P) of the lens. It is equal to the reciprocal of the focal length (i.e.,) P = 1/𝑓.
The SI unit of power of a lens is ‘dioptre’. If the length of the lens is expressed in metre, then power is in dioptre. A lens of focal length 100 cm has a power of 1 dioptre (i.e.,) 1 dioptre= 1m⁻¹ . Power of the dioptre. Lens is taken as +ve while the power of diverging or concave lens is –ve. Power can be found by using dioptometer.

Lenses in combination. When two or more lenses are used in combination, the converging or diverging power varies. The equivalent focal length F of two lenses of focal length in  𝑓₁ and 𝑓₂ contact is given by,1/F = 1/𝑓₂ +1/ 𝑓₂ , and so, the power of the combination P is, P =P₁ +P₂ .
Magnification in Combination. The total magnification is the product of the magnifications of the individual lenses. If are the magnification of lenses, the total magnification is
m=m₁ ×m₂ ×m₃ ×……. ×m_n .

MCQ Questions Light Reflection and Refraction Class 10 Science

Question. Study the following four experimental setups by four students A, B, C and D showing the incident ray to trace the path of a ray of light through a glass slab. Which of these will get the best result?   

(a) (A)
(b) (B)
(c) (C)
(d) (D)     

Question. A beam of light is incident through the holes on side A and emerges out of the holes on the other face of the box as shown in the figure.
Which of the following could be inside the box?

(a) Concave lens
(b) Rectangular glass slab
(c) Prism
(d) Convex lens     

Question. A student used a device (X) to obtain/focus the image of a well illuminated distant building on a screen (S) as shown below in the diagram. Select the correct statement about the device (X).   

(a) This device is a concave lens of focal length 8 cm.
(b) This device is a convex mirror of focal length 8 cm.
(c) This device is a convex lens of focal length 4 cm.
(d) This device is a convex lens of focal length 8 cm.     

Question. The focal length of the concave mirror in the following experimental set up is:  

(a) 12.4 cm
(b) 6.2 cm
(c) 6.0 cm
(d) 3.0 cm       

Question. Select the best experimental setup from the following options for tracing the path of a ray of light passing through a glass slab. 

(a) A
(b) B
(c) C
(d) D         

Question. If you focus the image of a distant object, whose shape is given below, on a screen using a convex lens,

the shape of the image of this object on the screen would be :

Question. The correct sequencing of angle of incidence,angle of emergence, angle of refraction and lateral displacement shown in the following diagram by digits 1, 2, 3 and 4 is: 

(a) 2, 4, 1, 3
(b) 2, 1, 4, 3
(c) 1, 2, 4, 3
(d) 2, 1, 3, 4   

Question. A student has traced the path of a ray of light through a glass slab as follows. If you are asked to label 1, 2, 3 and ∠, the correct sequencing of labeling ∠i, ∠e, ∠r and lateral displacement respectively is
(a) 2, 1, 3, 4
(b) 1, 2, 3, 4
(c) 1, 3, 2, 4
(d) 1, 3, 4, 2     

Question. A teacher sets up the stand carrying a convex lens of focal length 15 cm at 42.7 cm mark on the optical bench. He asks four students A, B, C and D to suggest the position of screen on the optical bench so that a distinct image of a distant tree is obtained almost immediately on it. The positions suggested by the students were as:
(A) 12.7 cm
(B) 29.7 cm
(C) 57.7 cm
(D) 72.7cm
The correct position of the screen was suggested by
(a) A
(b) B
(c) C
(d) D   

Question. When an object is kept within the focus of a concave mirror, an enlarged image is formed behind the mirror. This image is:
(a) real
(b) inverted
(c) virtual and inverted
(d) virtual and erect     

Question. A student obtained a sharp image of a candle flame placed at the distant end of the laboratory table on a screen using a concave mirror to determine its focal length.
The teacher suggested him to focus a distant building about 1 km far from the laboratory, for getting more correct value of the focal length. In order to focus the distant building on the same screen the student should slightly move the:
(a) mirror away from the screen
(b) screen away from the mirror
(c) screen towards the mirror
(d) screen towards the building   

Question. From the following diagram, select the incident rays whose paths after refraction have been correctly shown and can be used for locating the position of image formed by a convex lens. 

(a) 1 and 4
(b) 3 and 4
(c) 1, 3 and 4
(d) 1, 3, 4 and 5   

Question. Three students A, B and C focussed a distant building on a screen with the help of a concave mirror. To determine focal length of the concave mirror they measured the distances as given below:
Student A: rom mirror to the screen Student B: rom building to the screen Student C: rom building to the mirror Who measured the focal length correctly:
(a) Only A
(b) Only B
(c) A and B
(d) B and C   

Question. To determine the approximate focal length of the given convex lens by focussing a distant object (say, a sign board), you try to focus the image of the object on a screen. The image you obtain on the screen is always:
(a) erect and laterally inverted
(b) erect and diminished
(c) inverted and diminished
(d) virtual, inverted and diminished     

Question. A student very cautiously traces the path of a ray through a glass slab for different values of the angle of incidence (∠i). He then measures the corresponding values of the angle of refraction (∠r) and the angle of emergence (∠e) for every value of the angle of incidence. On analysing these measurements of angles, his conclusion would be:
(a) ∠i > ∠r > ∠e
(b) ∠i = ∠e > ∠r
(c) ∠i < ∠r < ∠e
(d) ∠i = ∠e < ∠r       

Question. In your laboratory you trace the path of light rays through a glass slab for different values of angle of incidence (3i) and in each case measure the values of the corresponding angle of refraction (3r) and angle of emergence (3e). On the basis of your observations your correct conclusion is:
(a) 3i is more than 3r, but nearly equal to 3e
(b) 3i is less than 3r, but nearly equal to 3e
(c) 3i is more than 3e, but nearly equal to 3r
(d) 3i is less than 3e, but nearly equal to 3r         

Question. To determine the approximate value of the focal length of a given concave mirror, you focus the image of a distant object formed by the mirror on a screen. The image obtained on the screen, as compared to the object is always:
(a) Laterally inverted and diminished
(b) Inverted and diminished
(c) Erect and diminished
(d) Erect and highly diminished 

Question. A student obtains a sharp image of the distant window (W) of the school laboratory on the screen (S) using the given concave mirror (M) to determine its focal length. Which of the following distances should he measure to get the focal length of the mirror? 

(a) MW
(b) MS
(c) SW
(d) MW – MS   

Question. A student traces the path of a ray of light through a rectangular glass slab for the different values of angle of incidence. He observes all possible precautions at each step of the experiment. At the end of the experiment, on analysing the measurements,which of the following conclusions is he likely to draw?
(a) ∠i = ∠e < ∠r
(b) ∠i < ∠e < ∠r
(c) ∠i > ∠e > ∠r
(d) ∠i = ∠e > ∠r     

Question. The image formed by a plane mirror is:
(a) virtual, behind the mirror and enlarged
(b) virtual, behind the mirror and of the same size as the object
(c) real, at the surface of the mirror and enlarged
(d) real, behind the mirror and of the same size as the object     

Question. Which of the following ray diagrams is correct for the ray of light incident on a concave mirror as shown in figure?

Question. Study the given ray diagrams and select the correct statement from the following:   

(a) Device X is a concave mirror and device Y is a convex lens, whose focal lengths are 20 cm and 25 cm respectively.
(b) Device X is a convex lens and device Y is a concave mirror, whose focal lengths are 10 cm and 25 cm respectively.
(c) Device X is a concave lens and device Y is a convex mirror, whose focal lengths are 20 cm and 25 cm respectively.
(d) Device X is a convex lens and device Y is a concave mirror, whose focal lengths are 20 cm and 25 cm respectively.

Question. Which one of the following materials cannot be used to make a lens?
(a) Water
(b) Glass
(c) Plastic
(d) Clay     

Question. A small bulb is placed at the focal point of a converging lens. When the bulb is switched on, the lens produces:
(a) a convergent beam of light
(b) a divergent beam of light
(c) a parallel beam of light
(d) a patch of coloured light   

Question. In torches, search lights and headlights of vehicles, the bulb is placed:
(a) between the pole and the focus of the reflector
(b) very near to the focus of the reflector
(c) between the focus and centre of curvature of the reflector
(d) at the centre of curvature of the reflector     

Question. Figure shows a ray of light as it travels from medium A to medium B. Refractive index of the medium B relative to medium A is:
(a) √3/2
(b) √2/√3
(c) 1/√2
(d) √2