Q.10 An opaque cylinder (shown below) is suspended in the path of a parallel beam of
light, such that its shadow is cast on a screen oriented perpendicular to the direction
of the light beam. The cylinder can be reoriented in any direction within the light
beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT
possible?
(A) P
(B) Q
(C) R
(D) S

The impossible shadow is R.​​

Concept overview

An opaque right circular cylinder can be rotated freely in a parallel beam of light, and its shadow is caught on a screen kept perpendicular to the beam.​
When the axis of the cylinder changes orientation with respect to the beam, the shadow on that plane can be a circle, an ellipse (or capsule‑like), or a rectangle, but discontinuous shapes with “cutouts” cannot occur.​

Option P – Circular shadow

• If the axis of the cylinder is parallel to the screen and perpendicular to the light beam, the light sees only the circular base and the cast shadow is a perfect circle, as in P.​

• This is exactly the usual “top view” of a cylinder kept upright, so P is definitely possible.​

Option Q – Capsule / rectangular‑with‑semicircles

• When the axis of the cylinder is parallel to the light beam but lies in the plane of the screen, the projection of the curved surface plus the two circular ends becomes a rectangle with semicircular ends (a capsule or stadium shape), like Q.​

• Such an elongated shadow is the standard side view of a cylinder and therefore Q is possible.

Option S – Long rectangle

• If the cylinder’s axis is parallel to the light beam and the cylinder is far from the screen, the two circular ends project almost on top of each other, and the dominating contribution is from the curved surface, giving a long rectangle on the screen, like S.​

• Thus a pure rectangular shadow is also a normal projection of a cylinder, so S is possible.​

Option R – Rectangle with a triangular notch

• Shadow R shows a rectangular band with a triangular cutout in the middle, i.e., the silhouette is not a single convex shape but looks like a rectangle minus a triangular piece.​

• A right circular cylinder has a smooth convex surface; any orthogonal projection (shadow on a plane) of such a convex body must also be a single convex region without indentations or notches.​

• No orientation of the cylinder in a parallel beam can remove only a central wedge of the rectangular shadow while keeping the rest, so R is not possible.

Final answer

• Shadow P – Possible (circular projection of the base).​

• Shadow Q – Possible (capsule‑shaped projection of side + ends).​

• Shadow S – Possible (rectangular projection of the curved surface).​

• Shadow R – Not possible, hence the correct option is (C) R.​