2021 A/L Physics Past Paper · Question 35 (English Medium)

Answer: (3) $60^\circ$

Given information

We know:

A ray in air meets a glass sphere. The angle of incidence is $60^\circ$.

The refractive index of the glass is $\sqrt{3}$.

What the question asks

We want: the total angle of deviation of the ray that comes out of the sphere.

Relevant theory

(2) For all rays of light of a given colour passing through two given media, the sine of the angle of incidence bears a constant ratio to the sine of the angle of refraction.

(1) If the first medium (a) is a vacuum or air the above ratio is known as the "absolute refractive index" of the second medium.

Required equations

$n = \dfrac{\sin i}{\sin r}$

$d_1 = i - r$

$D = d_1 + d_2$

Applying it to this question

First surface. The ray goes from air into glass, so $n = \dfrac{\sin 60^\circ}{\sin r}$.

$\sin r = \dfrac{\sin 60^\circ}{n} = \dfrac{\sqrt3 / 2}{\sqrt3}$

$0.5$

$\sin r = \dfrac{1}{2}$

$30$

$r = 30^\circ$

$60$

$\sin i_2 = n \sin 30^\circ = \sqrt3 \times \dfrac12$

$d_1 = d_2 = 60^\circ - 30^\circ$

Second surface. The two radii to the entry point and to the exit point are equal. They make an isosceles triangle with the chord.

So the ray meets the far surface at $30^\circ$ inside the glass. It leaves into air at $60^\circ$.

Each surface turns the ray by $60^\circ - 30^\circ = 30^\circ$, towards the same side.

All the angles are in degrees, so $D$ comes out in degrees.

Reasoning and calculation

$D = 30^\circ + 30^\circ = 60^\circ$.

This matches option (3).

Checks

$2 * (i - r)$

$a / b$

Does it make sense?

Glass bends the ray towards the normal, so $r$ is less than $i$. We found $30^\circ$ less than $60^\circ$.

The ray enters and leaves at the same angles, so the path inside is symmetric. The two turns are equal.

Conclusion

$D = 2(i - r) = 2(60^\circ - 30^\circ) = 60^\circ$

$r = 30^\circ$. Each surface turns the ray by $30^\circ$.

The total deviation is $60^\circ$. The answer is (3).

For a ray through a sphere, find $r$ at the first surface. The inside angle at the second surface is also $r$.

Each surface turns the ray by $i - r$. Add the two turns.

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