Question

A beam of light contains all wavelengths between 430 nm and 700 nm and is incident on a diffraction grating with 150 lines/mm. If two consecutive orders are overlapping, what can you say about the angles ? of the high and low wavelength light from the two orders?

a)

A. [?430nm]higher order<[?700nm]lower order

B. [?430nm]higher order>[?700nm]lower order

C. [?700nm]higher order<[?430nm]lower order

D. [?700nm]higher order=[?430nm]lower order

b) What is the lowest order that is overlapped by another order?

m= ________

c) What is the highest order for which the complete wavelength range of the beam is present?

m= ________

d) What is the greatest angle at which the light with the shortest wavelength appears?

________ degrees

Answer 1

a) B, 2nd highre order of 430nm > 1st lower order of 700nm

b) m = 1, 1st order is the lowest order which is overlapped by another order

c) m = 5, 5th order is the highest order which has complete wavelength range of the beam from red to voilet

d) Here, (a+b) Sin = n, or Sin / 150000 = n 430 x 10^-9

or  Sin = n 430 x 10^-9 x 150000 = n 645 x 10^-4 = 0.0645 n

or  Sin = 0.0645 (for n = 1)

Thus, = 3.7^o