Answer to Question #247855 in Classical Mechanics for Danjuma Adamu

Question

a system of grating has two wavelength 5.0 x 10^-7 and 5.2 x 10^-7m. the focal length is 2.0n and the grating separation is 2.0×10^-6m find the change in linear separatiom per unit increase in the specttal order of two wavelength

Answer 1

Write down the conditions for maxima and determine the angle:

$$d\sin\theta_1=m\lambda_1,\\ d\sin\theta_2=m\lambda_2.\\\space\\ \theta_1=\arcsin\frac{m\lambda_1}{d},\\\space\\ \theta_2=\arcsin\frac{m\lambda_2}{d}.$$

For the length between the grating and screen 2.0 m, find the change in linear separation:

$$\Delta z(m)=D(\tan\theta_2-\tan\theta_1)=\\\space\\ =D(\tan\arcsin\frac{m\lambda_2}{d}-\tan\arcsin\frac{m\lambda_1}{d})=\\\space\\ =2[\tan\arcsin(0.26m)-\tan\arcsin(0.25m)].$$