A monochromatic plane wave of speed c and wavelength λ is diffracted at a small aperture.

 Question 36

A monochromatic plane wave of speed c and wavelength λ is diffracted at a small aperture.

 

The diagram illustrates successive wavefronts.

After what time will some portion of the wavefront GH reach point P?

A 3λ / 2c                      B 2λ / c                                    C 3λ / c                                    D 4λ / c

 

 

 

Reference: Past Exam Paper – March 2017 Paper 12 Q28

 

 

 

Solution:

Answer: C.

Speed of wave = c

The distance between two successive wavefronts is equal to a wavelength.

So, the distance between wavefront GH and the wavefront containing point P is equal to 3 wavelengths (= 3λ).

Speed = distance / time

Time = distance / speed

Time = 3λ / c

A two-source interference experiment uses the apparatus shown. What is the main purpose of the single slit?

Question 35

A two-source interference experiment uses the apparatus shown.

What is the main purpose of the single slit?

A to make a narrow beam of light

B to make the same amplitude of light incident on each slit

C to provide coherent light

D to provide monochromatic light

Reference: Past Exam Paper – June 2018 Paper 12 Q29

Solution:

Answer: C.

The purpose of the single slit is to provide coherent light.

Coherent light have a constant phase difference.

Light is emitted in all directions (diverging) from the lamp. In the absence of the single slit, light from the lamp (diverging rays) would pass through the double slit, resulting in a variety of different phase differences at the screen.

Monochromatic light of wavelength λ is incident on two narrow slits S1 and S2, a small distance apart.

Question 34

Monochromatic light of wavelength λ is incident on two narrow slits S1 and S2, a small distance apart. A series of bright and dark fringes are observed on a screen a long distance away from the slits.

The n th dark fringe from the central bright fringe is observed at point P on the screen.

Which equation is correct for all positive values of n?

A S2P – S1P = nλ / 2

B S2P – S1P = nλ

C S2P – S1P = (n – ½)λ

D S2P – S1P = (n + ½)λ

Reference: Past Exam Paper – June 2017 Paper 13 Q28

Solution:

Answer: C. 

Dark fringes are formed when destructive interference occurs.

For destructive interference, the path difference should be 0.5λ, 1.5λ, 2.5λ, 3.5λ … [B is incorrect]

Consider option A.

Path difference = nλ /2

When n = 1, path difference = ½ λ

When n = 2, path difference = 2 λ / 2 = λ      [A is incorrect]

Consider option D.

When n = 1, path difference = (1 + ½) λ = 3λ / 2

This equation suggest that the first dark fringe occurs at 3λ / 2. [D is incorrect]

Consider option C.

When n = 1, path difference = (1 – ½) λ = λ / 2

This equation suggest that the path difference for the first dark fringe is equal to λ / 2 (= 0.5λ), which is correct.