(a) In Young’s double slit experiment, bright and dark fringes are obtained on the screen kept in front of a double slit due to the interference of light waves coming from the two slits. When the waves from both slits meet at a point on the screen, they can either constructively interfere, resulting in a bright fringe, or destructively interfere, resulting in a dark fringe. The expression for the fringe width can be derived from the path difference between the two waves, given by the formula for fringe width.

(b) The ratio of the intensities at minima to the maxima in the Young’s double slit experiment is 9:25. To find the ratio of the widths of the slits, we can use the relationship between intensity and slit width, leading to a calculation of the widths based on the given intensity ratio.

In Young's double slit experiment, light waves from two slits create a pattern of bright and dark fringes on a screen due to interference. When the waves meet, they can either add together (constructive interference) to form a bright fringe or cancel each other out (destructive interference) to create a dark fringe. The distance between these fringes, known as fringe width, can be calculated using the path difference between the waves from the two slits.

Understanding Fringe Width

The formula for fringe width (β) is given by:

β = λD/d

• λ = wavelength of light
• D = distance from the slits to the screen
• d = distance between the slits

This equation shows how the fringe width depends on the wavelength of the light and the geometry of the setup.

Intensity Ratio and Slit Widths

When the intensity ratio at the minima to maxima is given as 9:25, we can relate this to the widths of the slits. The intensity (I) is proportional to the square of the amplitude (A) of the light waves:

I ∝ A²

Let the widths of the slits be represented as w1 and w2. The intensity ratio can be expressed as:

I_min/I_max = (w1/w2)²

Given the intensity ratio of 9:25, we can set up the equation:

(w1/w2)² = 9/25

Taking the square root gives:

w1/w2 = 3/5

This means the ratio of the widths of the slits is 3:5, indicating how the slit sizes affect the interference pattern observed on the screen.