Question

monochromatic light is at normal incidence on a plane transmission grating. The first order maximum in the interference pattern is at an angle of 11.4 degrees. what is the angular position of the third order maximum? please give answer in units if degrees

Answer 1

All the maximums interference pattern are the same distance apart. Let's call this distance "y".

Let's call the distance between the grating and the screen "d".

The first maximum is y from the center line, so
tan (11.4) = y/d, m = 1

For small angles, tangent is approximately equal to sine.
sin (11.4) approx = y/d, m = 1

The fourth maximum is 3y from the center line, so
tan (x) = 3y/d
sin (x) approx= 3y/d
x = arcsin (3y/d)
x = arcsin (3 sin (11.4))
x = 36.37 degrees