The plane surface of a plano-convex lens of focal length 60 cm is silvered. A point object is placed at a distance 20 cm from the lens. Find the position and nature of the final image formed.

Solution

Given, a plane surface of plano-convex lens.
Focal length, f₁ = 60 cm
Object distance from the lens = 20cm

Let f be the focal length of the equivalent spherical mirror.

We have,

\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{m}} + \frac{1}{f_{1}}

i.e.,

\frac{1}{f} = \frac{2}{f_{1}} + \frac{1}{f_{m}}

Here,

f_{1} = + 60 cm

f_{m} = \infty

∴

\frac{1}{f} = \frac{2}{60} + \frac{1}{\infty} = \frac{1}{30}

\Rightarrow

f = + 30 cm

Now, the problem is reduced to a simple case where a point object is placed in front of a concave mirror.

Using mirror formula,

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

we have

\frac{1}{- 20} + \frac{1}{v} = \frac{1}{- 30}

\Rightarrow

v = 60 cm

and,
Magnification,

m = \frac{- v}{u} = \frac{- 60}{- 20} = + 3

The image is erect and virtual and is 3 times the size of object.

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Wave Optics

The plane surface of a plano-convex lens of focal length 60 cm is silvered. A point object is placed at a distance 20 cm from the lens. Find the position and nature of the final image formed.

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