Question

A monochromatic beam of light impinges normally on a grating and forms an image of the source slit 10 cm from the central image on a screen. The screen is 50 cm from the grating and is set parallel to it. The grating has 10,000 lines per inch. What is the wavelength of the light?

Answer 1

Solution:

First off, given that you have two measurements in cm why not get the lines per inch into lines per cm? At 2.54cm/in you should get 10,000 lines/in ~ 3937 lines/cm.

Next recall the diffraction equation:

d*sin = m*

Here we will need that angle theta. You have d given as the inverse of the lines per centimeter; that is, d = 1/3937 = 2.54*10^-4 cm spacing. We will solve for the m=1 (first order max). So it really comes down to trig to get that angle right?

Notice you have a triangle? 10 cm from center of screen and 50 cm away. This means you have opposite over adjacent lengths... ring a bell?! Exactly!

---> tan = 10/50 ---> = tan^-1 (10/50) ~ 11.3^o

So now plug all the info in and solve for lambda;

= 0.000254*sin(11.3) = 4.98 x 10^-5 cm = 498 nm (which is around bluish-green light)