A 5 cm long needle is placed 10 cm from a convex mirror of focal length 40 cm. Find the position, nature and size of image of the needle. What happens to the size of the image when the needle is moved further away from the mirror?

Solution

Given,
Length of the needle = 5 cm
Distance of object from the convex mirror, u = -10 cm
Focal length, f = 40 cm

Using the mirror formula,

\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{40} - \frac{1}{- 10} = \frac{1 + 4}{40} = \frac{5}{40}

\Rightarrow

v = \frac{40}{5} = 8 cm .

Now, magnification,

m = - \frac{v}{u}

When needle moves further away from the convex mirror, the image moves further behind the mirror towards the focus and size of the image decreases. When it is far off, it appears almost as a point image of the object.

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Wave Optics

A 5 cm long needle is placed 10 cm from a convex mirror of focal length 40 cm. Find the position, nature and size of image of the needle. What happens to the size of the image when the needle is moved further away from the mirror?

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