2021 A/L Physics Past Paper · Question 11 (English Medium)

Answer: (4) $P$, $Q$ and $R$ only.

What the question asks

Find which of the rays $P$, $Q$, $R$ and $S$ are refracted paths of rays from $A$.

The objects in the figure are the arrow $A$, a concave lens with a focus $F$ on each side, and four rays leaving the lens.

The plan: draw the rays from $A$ that we know, then see which of $P$, $Q$, $R$, $S$ match.

Relevant theory

Images formed by lenses can be constructed by using two rays from the topmost point of the object, one passing parallel to the axis of the lens and the other passing through the optical centre of the lens

The midpoint of a lens through which the rays are supposed to pass without any deviation is called the "optical centre" of the lens

Applying it to this question

The rays are the interaction between $A$ and the lens.

Read the figure: $A$ is above the axis. The dashed line is the plane of the lens. The rays $P$, $Q$, $R$, $S$ all start on that line.

So we ask which of them can come from $A$.

Variables we can read: the height of $A$ above the axis, and the height at which each ray leaves the lens.

$P$ leaves at the height of $A$. $Q$ leaves a little above the axis. $R$ leaves from the optical centre. $S$ leaves below the axis.

Reasoning and calculation

Take the three rays from $A$.

Ray 1. A ray from $A$ parallel to the axis. In a concave lens it bends away from the axis, as if it came from the focus $F$ on the side of $A$. It leaves at the height of $A$ and rises. That is $P$.

Ray 2. A ray from $A$ aimed at the far focus $F$. It leaves the lens parallel to the axis. It meets the lens a little above the axis. That is $Q$.

Ray 3. A ray from $A$ through the optical centre. It goes straight on and falls below the axis. That is $R$.

$S$ leaves the lens below the axis, on the straight line from $A$. A ray that meets the lens off-centre must be bent. $S$ is not bent. So $S$ is not a path.

Reading the options

The options list which of $P$, $Q$, $R$, $S$ are paths.

The rays $P$, $Q$ and $R$ are paths and $S$ is not. That matches option (4).

Why the other options fail

$Q$ is also a refracted ray from $A$. It comes from the ray aimed at the far focus.

$P$ is also a refracted ray from $A$. It comes from the ray parallel to the axis.

$S$ is not bent, so it cannot be a refracted ray. And $Q$ is left out.

$S$ is not bent, so it cannot be a refracted ray.

Checks

Does it make sense?

Trace $P$ and $R$ back with dotted lines. They meet at one point, above the axis, between $F$ and the lens. That point is the image of $A$.

For a concave lens the image is virtual, upright and smaller, so this is what we expect.

For all positions of the object the image is virtual, diminished, upright and forms between the focus and the lens.

Conclusion

$P$ is the ray parallel to the axis. $Q$ is the ray aimed at the far focus. $R$ is the ray through the optical centre.

$S$ is not bent, so it is not a path. The answer is (4).

For a lens, use the easy rays: parallel to the axis, through the centre, and aimed at the far focus.

Then check each drawn ray. A ray that meets the lens off-centre and is not bent cannot be right.

Exam tip