Question

Consider a diffraction grating with 600 lines per millimeter. Light from a light–emitting diode at λ = 830 nm with a bandwidth of ±10 nm is passed through a slit and a lens where it is collimated onto the grating at an angle of incidence of -5 degrees.

a. What is the range of angles in degrees to which the light is diffracted?

b. To make a spectrometer, I would like to place a camera chip with a 1–by– 1200 array of pixels, and a total length of 1 cm some distance, r away from the grating. If I would like the light from the LED to cover 50 pixels, what is the distance, r?

Answer 1

Since the incidence light is not perpendicular to the grating, the grating slit will have blazing effect in the difraction, also the range of difrracted light will depend upon the order of diffraction from the slit. For a blazed difraction the difraction equation is written as -

where,

n : difraction order

d : distance between two slits (1/N)

N : No of grating lines

= angle subtended by incidence light

= angle subtended by difracted light

Now, let's insert all the given values in the equation :

d = (1/600) mm = 1/6 x 10^-4 m

= 830 nm = 8.3 x 10^-7 m

= -5 degree

Now for

n = 0,  

n = 1,  

n = 2,  

a) Thus the angular spread in the difraction pattern will be 60 degree for first order difraction and 180 degree for second order difraction.

As given the chip with 1200 pixels in 1 cm with condition of the spead of difracted light at only at 50 pixels. The total linear spread length, y will be -

So the distance from the slit to the chip will be -

b) The distance will be 0.036 cm from slit to chip.