In a modified Young's double slit experiment, a monochromatic uniform and parallel beam of light of wavelength 6000 A o and intensity 10 / π Wm − 2 is incident normally on two apertures A and B of radii 0.001 m and 0.002 m respectively. a perfectly transparent film of thickness 2000 A o and refractive index 1.5 for the wavelength of 6000 A o is placed in front of aperture A ( see figure). Calculate the power ( in W ) received at the focal spot F of the lens. The lens is symmetrically place with respect to the apertures. Assume that 10% of the power received by each aperture goes in the original direction and is brought to the focal spot.

The power transmitted through A P A = 10 % o f 10 λ × π 0.001 2 = 10 100 × 10 λ × π × 10 - 6 = 10 - 6 w a t t The power transmitted through 'B' is P B = 10 % o f 10 λ × π 0.002 2 = 10 100 × 10 π × π × 4 × 10 - 6 = 4 × 10 - 6 w a t t Let ϕ be the phase difference t = introduced by film ϕ = 2 π λ x = 2 π λ × μ - 1 t = 2 π 6000 × 10 - 10 × 0.5 × 2000 × 10 - 10 ϕ = π 3 r e d i a n . The power received at F P = P A + P B + 2 P A P B cos ⁡ ϕ = 10 - 6 + 4 × 10 - 6 + 2 10 - 6 × 4 × 10 - 6 × 1 2 = 5 × 10 - 6 + 2 × 10 - 6 = 7 × 10 - 6 = 7 μ W P = 7 μ W

In a Young's double slit arrangement the separation between the two slits is 5 × 10 - 4 m and the screen is at a distance of 1 m from the slits. Light of wavelength 5000 A ° is used. A thin glass plate of thickness 1 . 5 × 10 - 6 m and refractive index 1 . 5 is placed in front of one of the two slits. Find the intensity of the interference pattern at the centre of the screen.

In case of interference I R = I 1 + I 2 + 2 I 1 I 2 cos ϕ Now, as for identical slits I 1 = I 2 = I , So, I R = 2 1 + cosϕ = 4 I cos 2 ϕ 2 But for central maxima, ϕ = 0 ° , and here I R = I 0 (given) I 0 = 4 I cos 0 ° = 4 I Hence, I R = I ∘ cos 2 ϕ 2 Now, When the glass plate is introduced, path between the waves at the position of central maxima will become ∆ x = μ - 1 t = 1 . 5 - 1 1 . 5 × 10 - 6 = 7 . 5 × 10 - 7 m ∴ ϕ = 2 π λ ∆ x = 2 π 5 × 10 - 7 × 7 . 5 × 10 - 7 = 3 π So, intensity at central maxima will now be I R = I ∘ cos 2 3 π 2 = I ∘ × 0 = 0

What is diffraction of light?

The phenomenon of bending of light around the corners of small obstacles or apertures and its spreading into the regions of the geometrical shadow is called diffraction of light.

HARD

12th West Bengal Board

IMPORTANT

Earn 100

Light of wavelength $500 nm$ falls from a distant source, on a slit $0.50 mm$ wide. Find the distance between the two dark bands on either side of the central bright band of the diffraction pattern observed on a screen placed $2 m$ from the slit

Important Questions on Wave Optics

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 17 - Wave Optics>EXERCISE 17>Q 22

Calculate the distance a beam of light of wavelength

500 nm

can travel without significant broadening if the diffraction aperture is

3 mm

wide.

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 17 - Wave Optics>EXERCISE 17>Q 25

Two wavelengths of sodium light

590 nm

and

596 nm

are used, in turn, to study the diffraction taking place at a single slit of aperture

2 \times 10^{- 4} m

.
The distance between the slit and the screen is

1.5 m

. Calculate the separation between the positions of the first secondary maxima of the diffraction pattern obtained in the two cases.

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 17 - Wave Optics>EXERCISE 17>Q 27

Assume that light of wavelength

6000 \overset{°}{A}

is coming from a star. What is the limit of resolution of a telescope where objective has a diameter of

100

inch.

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 17 - Wave Optics>EXERCISE 17>Q 3

Two coherent sources of light of intensity ratio n produce interference pattern. Prove that in that pattern

\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}} = \frac{2 \sqrt{n}}{1 + n}

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 17 - Wave Optics>EXERCISE 17>Q 4

In a modified Young's double slit experiment, a monochromatic uniform and parallel beam of light of wavelength $6000 \overset{o}{A}$ and intensity $(10 / π) {Wm}^{- 2}$ is incident normally on two apertures A and B of radii 0.001 m and 0.002 m respectively. a perfectly transparent film of thickness $2000 \overset{o}{A}$ and refractive index 1.5 for the wavelength of $6000 \overset{o}{A}$ is placed in front of aperture A ( see figure). Calculate the power ( in W ) received at the focal spot F of the lens. The lens is symmetrically place with respect to the apertures. Assume that 10% of the power received by each aperture goes in the original direction and is brought to the focal spot.

Question Image

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 17 - Wave Optics>EXERCISE 17>Q 6

The angular width of central maximum in the Fraunhofer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength

6000 \overset{\circ}{A}

. When the slit is illuminated by light of another wavelength, the angular width decreases by

30 %

. Calculate the wavelength of this light. The same decrease in the angular width of central maximum is obtained when the original apparatus is immersed in a liquid. Find the refractive index of the liquid.

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 17 - Wave Optics>EXERCISE 17>Q 23

Two slits are made

1 mm

apart and the screen is placed one metre away. What is the fringe separation when blue-green light of wavelength

500 nm

is used. What should the width of each slit be to obtain

10

maxima of the double slit pattern within the central maximum of the single slit pattern.

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 17 - Wave Optics>EXERCISE 17>Q 1

In a Young's double slit arrangement the separation between the two slits is

5 \times 10^{- 4} m

and the screen is at a distance of

1 m

from the slits. Light of wavelength

5000 \overset{°}{A}

is used. A thin glass plate of thickness

1.5 \times 10^{- 6} m

and refractive index

1.5

is placed in front of one of the two slits. Find the intensity of the interference pattern at the centre of the screen.

Light of wavelength 500 nm falls from a distant source, on a slit 0.50 mm wide. Find the distance between the two dark bands on either side of the central bright band of the diffraction pattern observed on a screen placed 2 m from the slit

Important Questions on Wave Optics

Learn and Prepare for any exam you want !

Light of wavelength $500 nm$ falls from a distant source, on a slit $0.50 mm$ wide. Find the distance between the two dark bands on either side of the central bright band of the diffraction pattern observed on a screen placed $2 m$ from the slit