Question

In a plane transmission grating, the angle of diffraction for the second-order principal maxima for wavelength \( 5000 \) Å is \( 30^\circ \). The number of lines per cm of the grating surface is:

• A. 10000
• B. 7500
• C. 5000
• D. 1500

Hint:

The **grating equation** is \( n \lambda = d \sin \theta \). The number of lines per cm is **\( 1/d \)**.

Answer 1

The Correct Option is C

The grating equation is given by:
\[ n \lambda = d \sin \theta \] where:
- \( n = 2 \) (second-order maximum)
- \( \lambda = 5000 \) Å = \( 5 \times 10^{-7} \) m
- \( \theta = 30^\circ \)
The grating element \( d \) is:
\[ d = \frac{n \lambda}{\sin \theta} = \frac{(2)(5 \times 10^{-7})}{\sin 30^\circ} \] \[ d = \frac{10 \times 10^{-7}}{0.5} = 2 \times 10^{-6} \text{ m} \] Since the number of lines per cm is:
\[ N = \frac{1}{d} = \frac{1}{2 \times 10^{-6}} = 5000 \text{ lines/cm} \]