Question

A monochromatic light of wavelength 6000Å is incident on the single slit of width 0.01 mm. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm, the linear width of the central maximum is :

• A. 60 mm
• B. 24 mm
• C. 120 mm
• D. 12 mm

Answer 1

The Correct Option is B

The linear width of the central maximum is given by the formula:

\[ W = \frac{2\lambda D}{a} \]

where:

• \(\lambda = 6000 \, \text{\AA} = 6 \times 10^{-7} \, \text{m}\)
• \(D = 20 \, \text{cm} = 0.2 \, \text{m}\)
• \(a = 0.01 \, \text{mm} = 1 \times 10^{-5} \, \text{m}\)

Substituting the values:

\[ W = \frac{2 \times 6 \times 10^{-7} \times 0.2}{1 \times 10^{-5}} = 24 \, \text{mm} \]

Thus, the correct answer is Option (2).