JEE Main · 2009 · 12 Apr 2009 · Offline · Geometrical Optics

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In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance

u

and the image distance

v

, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of

4 5^{\circ}

with the x-axis meets the experimental curve at P . The coordinates of P will be

(A) $(2 f, 2 f)$ ✓ Correct
(B) $(\frac{f}{2}, \frac{f}{2})$
(C)(f, f)
(D)(4f, 4f)

Answer: (A)

Solution

The

4 5^{\circ}

line through the origin is the locus

v = u

, so the point P marks the lens position where the image distance equals the object distance. For a convex lens this equality happens only when the object is at twice the focal length, and then the image also forms at twice the focal length, as the lens equation

\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

confirms with

u = v = 2 f

. The coordinates of P are therefore

(2 f, 2 f)

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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JEE Main · 2009 · 12 Apr 2009 · Offline · Geometrical Optics

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