Question

The grating in our lab has 13,400 line per inch. How many complete spectral order can be seen (400 nm to 700nm) when illumintaed by white light)

Answer 1

Use the equation

n*lambda = d*sin theta

d = grating space

n = number of order

lambda = wavelength

for complete spectral order

sin theta = 1

n*lambda = d*1

n = d/lambda

d = 13400 lines/in

1 in 2.54 cm

d = 4881.89 lines/cm

d = 1*10^-2 m/4881.89 = 2.048*10^-6 m

Now,

A.

lambda = 400 nm

n = d/lambda = 2.048*10^-6/(400*10^-9) = 5.12

n = 5 complete spectral order

B.

lambda = 700 nm

n = d/lambda = 2.048*10^-6/(700*10^-9) = 2.925

n = 2 complete spectral order

from A & B we can see that

for ehite light we can see 2 complete spectral order everywhere.

Let me know if you have any doubt.