HardPhysicsHigh School (11–12)OpticsNumericalConceptual

A prism of glass (n = 1.50) has angles 45°, 45° and 90°…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A prism of glass ( $n = 1.50$ ) has angles $45°$ , $45°$ and $90°$ . A ray goes into one of the two short faces at right angles, and reaches the long face, as in the left picture.

Two glass prisms in the shape of an isosceles right-angled triangle, light blue, refractive index 1.50, in air. In the left prism the right angle is at the lower left. An orange ray enters the vertical face at right angles, travels to the sloping face, meets it at 45 degrees, which is greater than the critical angle 41.8 degrees, is totally reflected, and leaves the lower face downward at right angles: it is turned through 90 degrees. In the right prism the sloping face is at the bottom. A purple ray enters it from below at right angles, meets the left slanting face at 45 degrees, is reflected horizontally, meets the right slanting face, is reflected again, and leaves downward through the bottom face parallel to its entering path: it is turned through 180 degrees. A 5 cm scale bar is drawn at the top right.

Find the critical angle for glass and air, and say what happens to the ray at the long face. Then the prism is put under water ( $n = 1.33$ ). Find the new critical angle, and the angle of refraction of the ray into the water at the long face. Finally find the smallest refractive index for which the prism still turns the ray through $90°$ in air.

Need a reminder? The key ideaShow

Snell's law is $n_1\sin\theta_1 = n_2\sin\theta_2$ , with the angles measured from the normal. The critical angle for light that goes from $n_1$ to a smaller $n_2$ is $\sin C = \dfrac{n_2}{n_1}$ . Light is totally reflected when the angle of incidence is larger than $C$ . In a material, $v = \dfrac{c}{n}$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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