JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Geometrical Optics

The graph between

\frac{1}{u}

and

\frac{1}{v}

for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of length is 1.5 and its both the surfaces have same radius of curvatures R. The value of R will be ______ cm.
(Where

u =

object distance,

v =

image distance)

Answer: 10

Solution

From the graph, point B corresponds to

\frac{1}{u} = - 0.10 cm^{- 1}

and

\frac{1}{v} = 0

.

This gives

u = - 10

cm and

v = \infty

, which means the object is at the focal point, so

f = 10

cm.

Using the lens maker's formula for a biconvex lens with equal radii:

\frac{1}{f} = (n - 1) (\frac{2}{R})

Substituting

f = 10

cm and

n = 1.5

\frac{1}{10} = (1.5 - 1) (\frac{2}{R}) = 0.5 \times \frac{2}{R} = \frac{1}{R}

Therefore

R = 10 cm

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Numerical answer

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