Q200S - Grating calculations

These questions give you practice in using the grating formula n λ = d  sinθn.
A grating with 500 lines per millimetre
1.  A grating is labelled '500 lines per mm'.  Calculate the spacing of the slits in the grating.

2.	Monochromatic light is aimed straight at the grating and is found to give a first-order maximum at 15°. Calculate the wavelength of the light source.

3.	Calculate the position of the first-order maximum when red light of wavelength 730 nm is shone directly at the grating.

4.	The longest visible wavelength is that of red light with λ = 750 nm. The shortest visible wavelength is violet where λ = 400 nm. Use this information to calculate the width of the angle into which the first-order spectrum is spread out when white light is shone onto the grating.

A grating with light of wavelength 550 nm
A grating is illuminated with a parallel beam of light of wavelength 550 nm. The first-order maximum is in a direction making an angle of 20° with the straight-through direction.

5.	Calculate the spacing of the grating slits.

6.	What would be the angle of the first-order maximum if a grating of slit spacing of 2.5 × 10–6 m were used with the same light source?

7.	Calculate the wavelength of light which would give a second-order maximum at θ = 32° with a grating of slit spacing 2.5 × 10–6 m.