Wave Optics — Practice

Question 1

Light of wavelength 600 nm in air enters a medium of refractive index 1.5. Find its wavelength and speed in the medium.

Accepted Answer

Frequency is unchanged, so divide both the speed and the wavelength by the refractive index. Answer: lambda = 400 nm; v = 2.0 x 10^8 m/s.

Question 2

In a double-slit experiment the slits are 0.5 mm apart and the screen is 1.0 m away. Find the fringe separation for light of wavelength 500 nm.

Accepted Answer

Use beta = lambda D / d, converting all lengths to metres. Answer: beta = 1.0 mm.

Question 3

Unpolarised light of intensity I falls on two polaroids whose pass axes are parallel. Find the intensity transmitted.

Accepted Answer

The first polaroid halves the intensity and the second passes it fully, since the angle between the axes is zero. Answer: I/2.

Question 4

In a double-slit experiment the fringe separation is 0.6 mm. What happens to it if the screen distance is doubled and the slit separation is halved?

Accepted Answer

Read the dependence directly from beta = lambda D / d. Answer: It becomes four times as large, 2.4 mm.

Question 5

Plane polarised light of intensity 40 W/m squared falls on a polaroid whose pass axis is at 60 degrees to the plane of polarisation. Find the transmitted intensity.

Accepted Answer

Apply Malus' law directly, since the light is already polarised. Answer: 10 W/m squared.

Question 6

Light of wavelength 500 nm falls on a slit of width 0.2 mm. Find the angular half-width of the central maximum.

Accepted Answer

The first minimum sets the edge of the central maximum, so use a sin(theta) = lambda. Answer: 2.5 x 10^-3 rad.

Question 7

In a two-slit pattern the maximum intensity is I_max. Find the intensity at a point where the path difference is lambda/4.

Accepted Answer

Convert the path difference to a phase of 90 degrees, then use the cosine squared expression. Answer: I_max/2.

Question 8

A slit of width 0.1 mm is illuminated by light of wavelength 600 nm and the pattern is viewed on a screen 2.0 m away. Find the linear width of the central maximum.

Accepted Answer

The central maximum spans two first-order minima, so its width is 2 lambda D / a. Answer: 2.4 cm.

Question 9

Two wavelengths 480 nm and 600 nm illuminate a double slit. Which orders of the two coincide first away from the centre?

Accepted Answer

Set n1 lambda1 = n2 lambda2 and reduce the ratio to its smallest whole numbers. Answer: The 5th bright fringe of 480 nm coincides with the 4th of 600 nm.

Practice — Wave Optics

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