2020 A/L Physics Past Paper · Question 32 (English Medium)

Answer: (3) only (A) and (C) are true.

What the question asks

Which of the three statements are true? Note that the statements are about the minimum deviation $D$ — not the general deviation $d$.

Relevant theory

It can be shown that, when the angle of incidence is increased starting from a small value, the emergent ray first moves in such a direction as to decrease the angle of deviation. Then it reaches a position where the deviation is minimum and then turns back to move in the direction of increasing the angle of deviation.

r₁ + r₂ = A

∴ i₁ + i₂ = A + d

This is Snell's law of refraction and it holds for electro-magnetic, sound and water waves.

Core idea: the deviation $d$ is a function of the angle of incidence $i_1$.

$D$ is its minimum value — a single number for a given prism ($A$, $n$) and colour of light.

If a change increases $d$ at every angle of incidence, the minimum $D$ also increases.

$\sin i_1 = n \sin r_1$

$r_2 = A - r_1$

$\sin i_2 = n \sin r_2$

$d = i_1 + i_2 - A$

Reading the options

The options are combinations of true statements: {A}, {A, B}, {A, C}, {B, C}, {A, B, C}. We judge all three, then match.

Reasoning and calculation

D increases as the refractive index of the material of the prism increases.

With $A$, $i_1$ unchanged, increasing $n$: $\sin r_1 = \sin i_1 / n$ decreases, so $r_2 = A - r_1$ increases; both factors in $\sin i_2 = n\sin r_2$ increase, so $i_2$ increases; $d = i_1 + i_2 - A$ increases. This holds for every $i_1$ — so the minimum of $d$, which is $D$, also increases.

A

D first decreases and then increases as the angle of incidence is gradually increased.

The book says: as the angle of incidence is gradually increased, the deviation first decreases, reaches a minimum, then increases. That minimum value is $D$ itself. So what varies with $i$ is $d$; $D$ is a fixed number — it does not "first decrease and then increase".

B

D increases as the angle of the prism increases.

With $n$, $i_1$ unchanged, increasing $A$ by $\Delta A$: $r_1$ stays the same, and $r_2 = A - r_1$ increases by $\Delta A$. Since the ray leaves a denser medium, $i_2 > r_2$; so in $\sin i_2 = n\sin r_2$, $i_2$ grows faster than $r_2$ ($\Delta i_2 > \Delta A$). In $d = i_1 + i_2 - A$, the growth in $i_2$ outpaces the growth in $A$, so $d$ increases — for every $i_1$; hence $D$ increases.

C

Why the false statement (B) is tempting: it correctly describes the book's $i$–$d$ behaviour (Figure 9.15) — but with $D$ written where $d$ belongs. The question bolds "minimum deviation $D$" exactly to flag this difference.

$37.2$

$r_1 = 30.7^\circ,\ r_2 = 29.3^\circ,\ i_2 = 47.2^\circ,\ d$

$58.6$

$r_1 = 26.8^\circ,\ r_2 = 33.2^\circ,\ i_2 = 68.6^\circ,\ d$

$51.8$

$r_1 = 30.7^\circ,\ r_2 = 39.3^\circ,\ i_2 = 71.8^\circ,\ d$

Numerical check ($d = i_1 + i_2 - A$, same $i_1 = 50^\circ$): $37.2^\circ \to 58.6^\circ$ ($n$ up), $37.2^\circ \to 51.8^\circ$ ($A$ up). Both changes increase $d$ — so its minimum $D$ increases too.

Why the other options fail

(C) is also true.

(B) is not true; (C) is missing.

(B) is not true; (A) is missing.

(B) is not true.

Conclusion

(A) and (C) are true; (B) describes the deviation $d$, not $D$ — the answer is (3).

"Minimum deviation $D$" and "deviation $d$" are different. $d$ varies with the angle of incidence; $D$ varies only with the prism's $n$, $A$ and the colour of light.

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