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Question 13

A ray of light enters an acrylic block and is refracted as shown in Figure 1.

Figure 1: Schematic showing a ray of light traveling from air into a flat horizontal surface of acrylic. The ray bends towards the normal as it enters the acrylic, so the angle of refraction r is smaller than the angle of incidence i. Both angles are measured with respect to a vertical dashed normal line.

a.

Explain why the ray of light is refracted towards the normal.

[2]
b.

Crown glass and zircon are transparent stones used in jewellery. Jewellers shape the stones so that light is reflected inside. Figure 2 shows the path of a ray of light that enters and leaves a shaped piece of crown glass. This ray of light is totally internally reflected.

Figure 2: Cross-section of a triangular gem of crown glass with a flat top and two inclined bottom sides meeting at a point. A ray of light drops vertically down into the gem through the top surface, hits the left inclined face at an angle of 45 degrees to the normal, undergoes total internal reflection, travels horizontally to the right inclined face, hits it at 45 degrees to the normal, undergoes total internal reflection again, and travels vertically up out of the top surface. The angle of incidence against each normal is labeled as 45 degrees, and the angle with the horizontal surface is also 45 degrees.

State the equation linking refractive index and critical angle.

[1]
c.

The critical angle of crown glass is 41∘41^\circ41∘. Show that the refractive index of crown glass is about 1.51.51.5.

[2]
d.

The refractive index of zircon is 1.91.91.9. Explain why rays of light inside a zircon gem are more likely to be totally internally reflected than those inside a crown glass gem.

[3]

Light and sound Questions

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