Question

Say you want to build an instrument to separate visible light from a light source into its colors. You decide to use a diffraction grating. Since this is suppose to be a scientific instrument, you want to be able to project the pattern of colors onto a screen , and measure the angles corresponding to each color. What range (lowest to highest) of d values (distance between adjacent slits) on your diffraction grating would give you a useful instrument? You'll need to make some reasonable assumptions and estimations, using for example, experience in a lab setting or playing with a grating in the classroom. State the details of your reasoning clearly.

Answer 1

we have the formula for diffraction as dsin=m

where is the wavelength and m is some non zero integer.

value of sin can not be greater than 1 which means the ratio of m/d can not be greater than 1. so will always be less than d. For visible light, maximum wavelength is around 700nm. so minimum value of d must be about 700nm.

another condition for diffraction is that the slit width must not be too larger than the wavelength. so maximum value of its width must be in the order of 10^-6 m or 1m.