Question

Using light from a monochromatic source to study diffraction in a single slit of width 0.1 mm, the linear width of central maxima is measured to be 5 mm on a screen held 50 cm away. The wavelength of light used is _______.
Fill in the blank with the correct answer from the options given below

• A. \(2.5 \times 10^{-7} \ \text{m}\)
• B. \(4 \times 10^{-7} \ \text{m}\)
• C. \(5 \times 10^{-7} \ \text{m}\)
• D. \(7.5 \times 10^{-7} \ \text{m}\)

Answer 1

The Correct Option is C

To find the wavelength of light used, we'll use the formula for the linear width of the central maximum in single-slit diffraction:

Width of central maximum (W) = (2λD) / a

Where:

• W is the linear width of the central maximum
• λ is the wavelength of light
• D is the distance from the slit to the screen
• a is the width of the slit

Given:

• a = 0.1 mm = 0.1 × 10^-3 m = 10^-4 m
• W = 5 mm = 5 × 10^-3 m
• D = 50 cm = 0.5 m

We need to find λ.

Rearranging the formula:

λ = (Wa) / (2D)

Substituting the given values:

λ = (5 × 10^-3 m × 10^-4 m) / (2 × 0.5 m)

λ = (5 × 10^-7 m²) / 1 m

λ = 5 × 10^-7 m

Therefore, the wavelength of light used is 5 × 10^-7 m.

The correct answer is:

Option 3: 5 × 10^-7 m