Answer to Question #122089 in Optics for Mio

Question

Diffraction grating A has 16 000 lines/cm, and diffraction grating B has 12 000 lines/cm. Light of the same wavelength is sent through both gratings to a screen located a distance L from the gratings. The spacing of the maxima for grating A is 3.46 cm. What is the spacing for the maximum for grating B?

Answer 1

Given:

$d_A=1/16 000 \text{ cm}^{-1}\\ d_B=1/12 000 \text{ cm}^{-1}\\ x_A=3.46\text{ cm}.$

Solution

The fringe spacing can be expressed as

$$x=\frac{\lambda L}{d},$$

where L - distance from the screen.

Thus, for A we have

$$x_A=\frac{\lambda L}{d_A},\\ \lambda L=x_Ad_A.$$

For B:

$$x_B=\frac{\lambda L}{d_B}=\frac{\lambda L}{d_B}=x_A\frac{d_A}{d_B}=3.46\cdot\frac{12000}{16000}=2.60\text{ cm}.$$