LIGHT - REFRACTION

1. Refraction of Light
2. Laws of Refraction
3. Refractive Index
4. Refraction through a Parallel Slab
5. Refractive Indices of Different Media
6. Principle of Reversibility of Light
7. Refraction through a Compound Slab
8. Apparent Depth of a Liquid
9. Total Internal Reflection
10. Refraction by Spherical Lenses
11. Image Formation by a Convex Lens
12. Image Formation by a Concave Lens
13. New Cartesian Sign Conventions
14. Lens Formula, Linear Magnification & Power of a Lens

Created by C. Mani, Principal, K V No.1, AFS, Jalahalli West, Bangalore

Refraction of Light:

Refraction is the phenomenon of change in the path (direction) of light as it travels from one transparent medium to another (when the ray of light is incident obliquely).

It can also be defined as the phenomenon of change in speed of light from one transparent medium to another.

Rarer

Rarer

Denser

N

N

Laws of Refraction:

I Law: The incident ray, the normal to the refracting surface at the point of incidence and the refracted ray all lie in the same plane.

II Law: For a given pair of media and for light of a given wavelength, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. (Snell’s Law)

μ

i

i

r

r

A

B

C

D

N

N

AB – Incident wavefront CD – Refracted wavefront XY – Refracting surface

E

F

G

X

Y

c, μ₁

v, μ₂

Denser

Rarer

Bending of Light

Refractive Index:

Refractive index of the 2^nd medium with respect to the 1^st medium is defined as the ratio of the sine of angle of incidence in the 1^st medium to the sine of angle of refraction in the 2^nd medium.

Refractive index of the 2nd medium with respect to the 1st medium is also defined as the ratio of the speed of light in the 1^st medium to the speed of light in the 2^nd medium.

(The constant ₁μ₂ is called refractive index of the medium, i is the angle of incidence and r is the angle of refraction.)

If the 1^st medium is vacuum or air, then the refractive index is called ‘absolute refractive index’.

If ‘c’ is the speed of light in air and ‘v’ is the speed of light in the medium, then the absolute refractive index is given by

Refraction through a Parallel Glass Slab:

Rarer medium (a)

Denser medium (b)

N

N

r₁

M

δ

y

But _aμ_b x _bμ_a = 1

It implies that i₁ = r₂ and i₂ = r₁ since i₁ ≠ r₁ and i₂ ≠ r₂.

μ

Rarer medium (a)

TIPS:

1. μ of optically rarer medium is lower and that of a denser medium is higher.
2. μ of denser medium w.r.t. rarer medium is more than 1 and that of rarer medium w.r.t. denser medium is less than 1. (μ_air = μ_vacuum = 1)
3. In refraction, the velocity and wavelength of light change.
4. In refraction, the frequency and phase of light do not change.
5. _aμ_m = c_a / c_m and _aμ_m = λ_a / λ_m

Refractive Index of different media

Rarer (a)

N

Denser (b)

or

If a ray of light, after suffering any number of reflections and/or refractions has its path reversed at any stage, it travels back to the source along the same path in the opposite direction.

A natural consequence of the principle of reversibility is that the image and object positions can be interchanged. These positions are called conjugate positions.

μ

Principle of Reversibility of Light: (Not in Syllabus)

Refraction through a Compound Slab: (Not in Syllabus)

Rarer (a)

Rarer (a)

Denser (b)

N

N

μ_b

Denser (c)

μ_c

N

_aμ_b x _bμ_c x _cμ_a = 1

_aμ_b x _bμ_c = _aμ_c

or

_bμ_c = _aμ_c / _aμ_b

or

μ_a

μ_c > μ_b

​

Apparent Depth of a Liquid: (Not in Syllabus)

Rarer (a)

Denser (b)

O

O’

N

μ_b

or

Apparent Depth of a Number of Immiscible Liquids:

Apparent Shift:

Apparent shift = h_r - h_a = h_r – (h_r / μ)

= h_r [ 1 - 1/μ]

TIPS:

1. If the observer is in rarer medium and the object is in denser medium then h_a < h_r. (To a bird, the fish appears to be nearer than actual depth.)
2. If the observer is in denser medium and the object is in rarer medium then h_a > h_r. (To a fish, the bird appears to be farther than actual height.)

μ_a

Total Internal Reflection: (Not in Syllabus)

Total Internal Reflection (TIR) is the phenomenon of complete reflection of light back into the same medium for angles of incidence greater than the critical angle of that medium.

N

N

N

N

O

r = 90°

Rarer (air)

Denser (glass)

μ_g

μ_a

Conditions for TIR:

1. The incident ray must be in optically denser medium.
2. The angle of incidence in the denser medium must be greater than the critical angle for the pair of media in contact.

Relation between Critical Angle and Refractive Index: (Not in Syllabus)

Critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.

or

or

Also

Red colour has maximum value of critical angle and Violet colour has minimum value of critical angle since,

Applications of T I R:

1. Mirage formation
2. Looming
3. Totally reflecting Prisms
4. Optical Fibres
5. Sparkling of Diamonds

Refraction by Spherical Lenses

Lenses whose refracting surfaces are spherical are called ‘spherical lenses’.

A spherical lens whose refracting surfaces are bulging outwards at the centre is called a ‘double convex lens’. It is thicker in the middle compared to the edges.

A spherical lens whose refracting surfaces are curved inwards at the centre is called a ‘double concave lens’. It is thinner in the middle compared to the edges.

Different types of Spherical Lenses

Double Convex

Double Concave

Plano-convex

Plano-concave

Convexo-concave

Concavo-Convex

Meniscus lenses

First Principal Focus:

First Principal Focus is the point on the principal axis of the lens at which if an object is placed, the image would be formed at infinity.

F₁

F₂

Second Principal Focus:

Second Principal Focus is the point on the principal axis of the lens at which the image is formed when the object is kept at infinity.

F₂

F₁

Concave Lens

Convex Lens

Optic Centre (O) is the central point of a lens.

Centre of curvature (C) is the centre of the imaginary sphere from which spherical lens is cut out. There are two centres of curvature on either side of the lens.

Radius of curvature (R) is the distance between the optic centre and the centre of curvature.

Principal axis (XPX’) is the line passing through the optic centre and the centre of curvature and extending to ∞. It is the normal to the lens at the pole.

Principal Focus (F) is the point on the principal axis at which the incident rays of light parallel to principal axis either really pass through or appear to pass through after getting refracted from the lens. There are two foci for the lens.

Focal length (f) is the distance between the optic centre and the principal focus.

Radius of curvature is approximately twice the focal length. R ≈ 2f

Aperture (MN) is the diameter of the refracting surface. Note that it is not the diameter of the sphere from which the lens is cut out.

Rays to be considered for drawing Ray Diagram

The intersection of at least two refracted rays give the position of image of the point object.

Any two of the following rays can be considered for locating the image.

1. A ray parallel to the principal axis, after refraction from a convex lens, passes through the principal focus on the other side of the lens. In case of a concave lens, the ray appears to diverge from the principal focus on the same side of the lens.

2. A ray passing through the principal focus of a convex lens or a ray which is directed towards the principal focus of a concave lens, after refraction, will emerge parallel to the principal axis.

3. A ray passing through the optic centre of a convex or concave lens, after refraction, will emerge without any deviation.

Image formation by a convex lens

1) When object is placed at infinity:

•

O

B

Parallel rays from ∞

1. Position of image: At F₂
2. Nature of image : Real & inverted

iii) Size of image : Very small

(Highly Diminished)

2) When object (AB) is placed beyond C₁ (2F₁):

•

O

1. Position of image: Between C₂ (2F₂) & F₂
2. Nature of image : Real & inverted

iii) Size of image : Smaller than object

(Diminished)

3) When object (AB) is placed at C₁ (2F₁):

•

O

1. Position of image: At C₂ (2F₂)
2. Nature of image : Real & inverted

iii) Size of image : Same size as that of the object

•

O

4) When object (AB) is placed between C₁ (2F₁) & F₁:

1. Position of image: Beyond C₂ (2F₂)
2. Nature of image : Real & inverted

iii) Size of image : Larger than object

(Enlarged)

5) When object (AB) is placed at F₁:

•

O

1. Position of image: At ∞
2. Nature of image : Real & inverted

iii) Size of image : Very large

(Highly enlarged)

Parallel rays meet at ∞

6) When object (AB) is placed between F₁ & O: (Simple Microscope)

•

O

1. Position of image: On the same side as that of the object
2. Nature of image : Virtual & erect

iii) Size of image : Larger than the object

Image formation by a convex lens for different positions of the object

Image formation by a concave lens

•

O

1. Position of image: On the same side as that of the object
2. Nature of image : Virtual & erect

iii) Size of image : Smaller than the object

Sign Conventions for Refraction by Spherical Lenses (New Cartesian Sign Convention)

1. The object is always placed to the left of the lens. i.e. the incident rays from the object always move from left to right.
2. All distances parallel to the principal axis are measured from the optic centre (O) of the lens.
3. All the distances measured to the right of the optic centre (along +ve x-axis) are taken +ve while those measured to the left of the optic centre (along - ve x-axis) are taken –ve.
4. Distances measured perpendicular to and above the principal axis (along +ve y-axis) are taken +ve while those measured below the principal axis (along –ve y-axis) are taken –ve.

Note:

While solving numerical problems, new Cartesian sign convention must be used for substituting the known values of u, v, f, h and R.

•

O

- ve

+ ve

+ ve

- ve

•

O

M

Lens Formula

u – object distance

v – image distance

f – focal length of the mirror

Linear Magnification:

Linear magnification produced by a lens is defined as the ratio of the size of the image to the size of the object.

Magnification in terms of v and f:

Magnification in terms of u and f:

More of Refraction in Higher Class…

Magnification produced by a lens is also defined as the ratio of the image distance to object distance.

Power of a Lens:

Power of a lens is its ability to bend a ray of light falling on it and is reciprocal of its focal length.

When f is in metre, power is measured in Dioptre (D).