Question

When an object is placed at a distance of 15 cm from a concave mirror, image is formed at 10 cm in front of the mirror. Calculate focal length and nature of image.

Answer 1

Answer:

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Answer 2

Answer:

The focal length of the concave mirror is -6cm and the nature of the image is real and inverted.

Explanation:

We will solve this question through the mirror formula.i.e.

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$        (1)

Where,

f=focal length of the mirror

v=image distance from the mirror

u=object distance from the mirror

From the question we have,

v=-10cm (negative sign as it is placed in front of the mirror and the image is real)

u=-15cm (negative sign as it is placed in front of the mirror)

By substituting the value of v and u in equation (1) we get;

$\frac{1}{f}=\frac{1}{-10}+\frac{1}{-15}$

$f=\frac{-15\times -10}{-25}=-6cm$      (2)

Now lets calculate the magnification of the mirror i.e.

$m=\frac{-v}{u}=\frac{-1\times -10}{-15}=\frac{-2}{3}$     (3)

The negative magnification indicates that the image is inverted.

Hence, the focal length of the concave mirror is -6cm and the nature of the image is real and inverted.