JEE Advanced 2018 · Paper 2 · Physics Q4

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PhysicsMultiple correct+4 / -2Question 4 of 54

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$ , as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

Concave mirror with its principal axis horizontal. A right-angled triangular wire sits on the axis in front of the mirror: its vertical side stands at distance f/2 from the pole and its hypotenuse slopes down to meet the axis at the focus f, making 45° with the axis.

Dashed image: a vertical segment standing on the axis with a slanted side meeting the axis to its left at angle α, where α > 45° (a taller, steeper triangle).

Dashed image: a vertical segment rising from the axis, from whose top a slanted dashed line runs up-left to an arrow marked ∞.

Dashed image: a flat triangle with a short vertical side on the axis and a slanted side meeting the axis to the left at angle α, where 0 < α < 45°.

Dashed image: a vertical segment rising from the axis, from whose top a horizontal dashed line runs left to an arrow marked ∞.

Answer and worked solution

Official answer: D

Vertical side. It stands at distance $f/2$ , inside the focal length. Using the real-is-positive form $\frac1v+\frac1u=\frac1f$ :
$\frac1v=\frac1f-\frac2f=-\frac1f\implies v=-f,$
a virtual image a distance $f$ behind the mirror, with magnification $\dfrac{|v|}u=2$ . The side has height $f/2$ (from the $45^\circ$ angle), so its image is a vertical line of height $f$ .

Hypotenuse. A point at distance $x$ from the pole ( $f/2\le x\le f$ ) has height $h=f-x$ . Its image is virtual, a distance
$|v|=\frac{xf}{f-x}\ \text{behind the mirror},\qquad m=\frac{|v|}x=\frac f{f-x},$
so the image height is $mh=f$ , the same for every point. The image of the hypotenuse is a horizontal line at height $f$ . It runs from distance $f$ behind the mirror to infinity, since the point at the focus images at infinity.

Shape. A vertical segment whose top joins a horizontal line going off to infinity. That is (D).

(D)

Topics:Spherical mirrors

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JEE Advanced 2018 · Paper 2, Physics question 4