Diffraction, diffraction gratings, refraction.

Course work 8 (2011-12)

DIFFRACTION, DIFFRACTION GRATINGS, REFRACTION.

1) Parallel light is incident normally onto a diffraction grating. For light of wavelength 589 nm the first order interference maxima are observed in directions of 22^o to the straight through direction.

a) Calculate the number of slits per mm in the grating.

b) What wavelength of light would give a first order maximum at 24.3^o?

4 marks)

2) Monochromatic light of wavelength 500nm falls normally onto a diffraction grating with 600 lines mm^-1. Calculate the angular position θ of the first order spectrum on each side of the normal. What is the maximum number of bright fringes seen on each side of the normal? (4 marks)

3) Parallel white light is incident normally onto a diffraction grating. It is found that, at 30⁰ to the straight-through direction, a maximum for yellow light (of wavelength 6.0 x 10^-7 m) coincides with a maximum for blue light (of wavelength 4.8 x 10^-7) m. In this direction the order (n) of the interference maximum for blue light is one more than for yellow light. Find the spacing of the lines of the diffraction grating.

(4 marks)

4). The diagram below shows plane waves on the water in a shallow tank approaching a gap between two obstacles, M and N.

		M
					screen
			N

Sketch diagrams to show the wave-fronts to the right of MN under the following conditions:

a) when the wavelength is greater that the width of the gap

b) when the wavelength is much less that the width of the gap.

State with reasons in which of these cases can the behaviour of light only be explained by assuming it has a wave nature? (6 marks)

5) Parallel white light is incident normally onto a single slit. In the resulting diffraction pattern it is observed that the first minimum for red light of wavelength 650 nm occurs at an angle of 15⁰ to the incident beam. Evaluate the width of the slit. (3 marks)

6) A ray of white light enters a glass block at an angle of incidence of 30^o. What is the angle in the glass between red light with refractive index 1.65 and blue light of refractive index 1.68? (3 marks)

7) A ray of light travelling in water of refractive index 1.33 strikes the surface at an angle of incidence of 40⁰. Find the angle θ_a at which it emerges into air.

A layer of oil of refractive index 1.44 is poured onto the surface of the water. Obtain the angle of refraction of the ray in the oil and show that the beam still emerges into air at the same angle θ_a. (6 marks)

8) Orange light of wavelength 600 nm travels from air into a glass block of refractive index 1.5.

Find a) the speed b) the wavelength c) the frequency of the light when inside the glass. (4 marks)

9) Explain what is meant by the critical angle for light incident onto the interface between two media?

Calculate the critical angle between the following media:

a). glass-air

b). water-air

c).glass-water

(Take, ).

Draw sketches showing the path of a ray of light incident on each interface at the critical angle. (6 marks)

10) A small luminous object at the bottom of a pool of water 2.00 m deep, emits rays of light in all directions. Explain why a circular area of light is formed on the surface of the water. Evaluate the radius of this circle of light if the refractive index of water is 4/3. (4 marks)

11) Some modern optical devices are made from glass whose refractive index changes with distance from the front surface. Consider such a 1 cm thick glass slab where the refractive index varies linearly from 1.5 at the front surface to 1.6 at the rear surface. Obtain an expression for how long it takes for a beam of light incident normally on the front surface to travel a distance x inside the slab. Evaluate the time taken for the light beam to travel completely through the glass.

(Hint: write down an algebraic expression for the refractive index as a function of distance inside the slab, then consider time taken for light to travel a distance dx) (4 marks)

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