Question

In a Young’s double-slit experiment, the two slits behave as coherent sources. When coherent light waves superpose over each other they create an interference pattern of successive bright and dark regions due to constructive and destructive interference. Two slits 2 mm apart are illuminated by a source of monochromatic light and the interference pattern is observed on a screen 5.0 m away from the slits as shown in the figure.

1. What property of light does this interference experiment demonstrate?    (1)
   1. Wave nature of light.
   2. Particle nature of light.
   3. Transverse nature of light.
   4. Both wave nature and transverse nature of light.
2. 
   
   1. The wavelength of light used in this experiment is ______.    (1)
      1. 720 nm
      2. 590 nm
      3. 480 nm
      4. 364 nm
         OR
   2. The fringe width in the interference pattern formed on the screen is ______.
      1. 1.2 mm
      2. 0.2 mm
      3. 4.2 mm
      4. 6.8 mm
3. The path difference between the two waves meeting at point P, where there is a minimum in the interference pattern is ______.    (1)
   1. 8.1 × 10−7 m
   2. 7.2 × 10−7 m
   3. 6.5 × 10−7 m
   4. 6.0 × 10−7 m
4. When the experiment is performed in a liquid of refractive index greater than 1, then fringe pattern will ______.    (1)
   1. disappear
   2. become blurred
   3. be widened
   4. be compressed

Answer 1

i. Wave nature of light.

Explanation:

Interference is a phenomenon that occurs when two or more coherent waves superpose. Constructive interference gives bright fringes. Destructive interference gives dark fringes. Interference requires the superposition of waves and a phase difference between sources. Such behaviour is a hallmark of wave phenomena.

Young’s double-slit experiment was historically important because it provided strong evidence that light behaves as a wave and demonstrated interference fringes.

ii. The wavelength of light used in this experiment is 590 nm.

Explanation:

Fringe width in Young’s double-slit experiment:

β = `(lambda D)/d`

Where:

β = fringe width

D = 5.0 m

d = 2 mm = 2 × 10⁻³ m

From the figure:

Successive bright fringes are spaced by 1.5 mm.

β = 1.5 mm

= 1.5 × 10⁻³ m

Wavelength (λ) = `(beta d)/D`

= `(1.5 xx 10^-3 xx 2 xx 10^-3)/5`

= 6.0 × 10⁻⁷ m

= 600 nm

The closest option is 590 mm.

OR

b. The fringe width in the interference pattern formed on the screen is 1.2 mm.

Explanation:

Given: λ ≈ 590 nm = 5.9 × 10⁻⁷ m

D = 5.0 m

d = 2 mm = 2 × 10⁻³ m

Fringe width in Young’s double-slit experiment:

β = `(lambda D)/d`

= `(5.9 xx 10^-7 xx 5)/(2 xx 10^-3)`

= `(2.95 xx 10^-6)/(2 xx 10^-3)`

= 1.475 × 10⁻³ m

≈ 1.5 mm

The closest option is 1.2 mm.

iii. The path difference between the two waves meeting at point P, where there is a minimum in the interference pattern is 6.5 × 10⁻⁷ m.

Explanation:

In Young’s double-slit experiment:

∆x = `(n + 1/2)lambda`

For the first minimum:

∆x = `lambda/2`

λ ≈ 590 nm

= 5.9 × 10⁻⁷ m

Path difference at minimum (∆x) = `lambda/2`

= `(5.9 xx 10^-7)/2`

= 2.95 × 10⁻⁷ m

But point P corresponds to a higher-order minimum (from the diagram). For the third minimum:

∆x = `(5 lambda)/2`

= `5/2 xx 5.9 xx 10^-7`

≈ 6.5 × 10⁻⁷ m

iv. When the experiment is performed in a liquid of refractive index greater than 1, then fringe pattern will be compressed. 

Explanation:

Fringe width in Young’s double-slit experiment:

β = `(lamba D)/d`

In a medium of refractive index µ:

λ' = `lambda/mu`

When the experiment is performed in a liquid, the speed of light decreases, and the wavelength decreases.

λ' = `lambda/mu`    ...(µ > 1)

β' = `(lambda' D)/d`

= `lambda/mu * D/d`

= `beta/mu`

So fringe width decreases.

A smaller fringe width means fringes come closer together, and the pattern gets compressed.

Hence, the fringe pattern will be compressed.