Derive the expression for the intensity at a point where interference of light occurs. Arrive at the conditions for maximum and zero intensity.

Let the two waves S 1 and S 2 from the two coherent sources interfere at a point P. Let their amplitudes be a and the initial phase difference between them be ϕ . Then the displacements produced by S 1 and S 2 will be given as: y 1 = a cos ω t ....(i) y 2 = a cos ωt + ϕ ....(ii) The intensity produced by each wave, I 0 ∝ a 2 ....(iii) The resultant displacement at point P will be: y = y 1 + y 2 y = a cos ω t + cos ω t + ϕ y = 2 a cos ϕ 2 cos ω t + ϕ 2 ......(iv) From (iii), it is clear that the amplitude of the resultant displacement is 2 a cos ϕ 2 and therefore the intensity at that point will be: I ∝ 4 a 2 cos 2 ϕ 2 On using (iii), we get: I = 4 I 0 cos 2 ϕ 2 .....(v) Where I 0 is the intensity of each of the individual sources. Using (v) , For ϕ = 0 , ± 2 π , ± 4 π . . . . . , the intensity will be maximum and given by: I = 4 I 0 For ϕ = ± π , ± 3 π , ± 5 π . . . . , the intensity will be zero: I = 0

Light travels in a straight line because

diffraction effect is negligible

it is not absorbed by atmosphere

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Earn 100

The radius of curvature of curved surface at a thin planoconvex lens is $10 cm$ and the refractive index is $1.5$ . If the plane surface is silvered then the focal length will be:

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Important Questions on Optics

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Optics>Exercise>Q 47

An object of size

3.0 c m

is placed

14 c m

in front of a concave lens of focal length

21 c m

. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Optics>Exercise>Q 48

A beam of light converges at a point

P

. Now a lens is placed in the path of the convergent beam

12 c m

from

P

. At what point does the beam converge if the lens is a convex lens of focal length

20 c m

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Optics>Exercise>Q 49

What is the focal length of a convex lens of focal length

30 c m

in contact with a concave lens of focal length

20 c m

? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

HARD

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Optics>Exercise>Q 50

A compound microscope consists of an objective lens of focal length

2.0 c m

and an eyepiece of a focal length

6.25 c m

separated by a distance of

15 c m

. How far from the objective should an object be placed in order to obtain the final image at the least distance of distinct vision

(25 cm)

and what is the magnifying power of the microscope?

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Optics>Exercise>Q 51

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall

3 m

away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Optics>Exercise>Q 52

Double-convex lenses are to be manufactured from a glass of refractive index

1.55

, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be

20 c m

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Optics>Exercise>Q 53

A short-sighted man can read printed matter distinctly when it is held

15 cm

from his eye. Find the focal length of the glasses which he must use if he wishes to read with ease a book at a distance of

60 cm

EASY

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 6 - Optics>Exercise>Q 54

The refractive index of the material of a concave lens is

n

. It is immersed in a medium of refractive index

n_{1}

. A parallel beam of light is incident on the lens. Trace the path of the emergent rays in each of the following cases:(i)

n_{1} = n

(ii)

n_{1} > n

and (iii)

n_{1} < n

The radius of curvature of curved surface at a thin planoconvex lens is 10 cm and the refractive index is 1.5. If the plane surface is silvered then the focal length will be:

Important Questions on Optics

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The radius of curvature of curved surface at a thin planoconvex lens is $10 cm$ and the refractive index is $1.5$ . If the plane surface is silvered then the focal length will be: