Question

An object placed at a distance of 15cm of convex mirror of focal length 30 cm.find position and nature of image

Answer 1

The image is formed at a distance of 10 cm from the mirror and the nature of the image is virtual and erect.

Given,

An object is placed at a distance of 15cm from the convex mirror.

The focal length of the mirror is 30 cm.

To Find,

The position and nature of the image.

Solution,

Using the mirror formula

1/f = 1/u+1/v

where

f is the focal length of the mirror = 30 cm

u is the object distance = -15 cm

v is the image distance.

1/30 = -1/15+1/v

1/30+1/15 = 1/v

1/v = 3/30

v = 10 cm

Hence, the image is formed at a distance of 10 cm from the mirror and the nature of the image is virtual and erect.

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Answer 2

Step 1: Given data

object distance, $u=-15cm$

focal length of mirror$=30cm$

image distance, $v=?$

nature of image$=?$

Step 2: Calculating the position and nature of image

We know that,

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

$\frac{1}{30}=\frac{1}{-15} +\frac{1}{v}$

$\frac{1}{v}=\frac{1}{30} +\frac{1}{15}=\frac{1+2}{30}=\frac{3}{30} =\frac{1}{10}$

$v=10cm$

Hence, the image is formed at a distance of $10cm$ from the mirror; and the nature of the image will be virtual and erect.

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