2020 A/L Physics Past Paper · Question 08 (English Medium)

Answer: (4) $D$

What the question asks

We want: after refraction through the converging lens, at which point ($A$–$E$) does the oblique ray $XY$ strike the screen $S$?

Relevant theory

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

Planes passing through the focal points of a lens normal to the principal axis are called focal planes.

Converge to a point on the focal plane on the opposite side in case of a convex lens.

Applying it to this question

What the figure shows:

A converging lens $L$.

A principal focus $F$ on each side (distance $f$ from the lens).

The focal plane through the right-hand focus.

A screen $S$ beyond $F$, with points $A$ (on the axis) to $E$ equally spaced.

An oblique ray $XY$ above the axis, sloping downward, that strikes the lens at $Y$.

Thinking it through:

$XY$ is not parallel to the axis.

So it does not pass through $F$.

All rays parallel to $XY$ belong to the same parallel beam.

After refraction they all meet at one point on the focal plane.

Reasoning and calculation

Reading the figure (in units of $f$):

$Y$ is above the axis by about $0.32f$.

$XY$'s slope is about $0.35$ downward per unit length.

The screen is about $2.1f$ from the lens.

The spacing between consecutive points is about $0.36f$.

The rule:

(i) A ray through the optical centre does not bend.

(ii) An oblique parallel beam converges at one point on the focal plane.

So the construction ray through the optical centre, parallel to $XY$, marks that point $Q$.

$-0.35f$

$y_Q = -0.35 \times 1\,f$

$\frac{0.32 + 0.35}{1} = 0.67$

$-1.09f$

$y_S = 0.32 - 0.67 \times 2.1$

$3$

$\frac{1.09}{0.36} \approx 3$

$D$

$A \to B \to C \to D$

Reading the options

The third point below the axis is $D$.

Option (4).

Why the other options fail

$A$ is on the principal axis.

Only a ray parallel to the axis converges at $F$, which is on the axis.

$B$ is where the ray from $Y$ through $F$ would land.

$XY$ is not parallel to the axis.

$C$ is where the construction ray touches the screen.

But the two rays actually meet on the focal plane.

$E$ comes from bending the ray too far.

The ray must pass through $Q$ itself.

Checks

Does it make sense?

The converging lens bends the ray towards the axis.

The refracted slope ($0.67$) is steeper than the incoming slope ($0.35$). ✓

$Q$ is below the axis, because $XY$ slopes downward. ✓

Since the screen is beyond $F$, the ray must cross the axis and land below it. ✓

Conclusion

The construction ray through the optical centre, parallel to $XY$, marks $Q$ on the focal plane.

The refracted ray from $Y$ through $Q$ reaches the screen at $D$.

The answer is (4).

For an oblique ray:

Draw a line through the optical centre parallel to it.

The refracted ray passes through the point where that line crosses the focal plane.

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