Question

If an object is placed 10 cm infront of a concave mirror of focal length 20 cm, the image distance will be ___.​

Answer 1

Given:

• Object distance (u) = -10cm
• Focal length (f) = -20cm

To find:

• The image distance.

Solution:

★ By using mirror formula,

• 1/v + 1/u = 1/f

➯ 1/v = 1/f - 1/u

➯ 1/v = -1/20 + 1/10

➯ 1/v = -1 + 2/20

➯ 1/v = 1/20

➯ v = 20cm

Hence, the image distance is 20cm behind the mirror.

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Answer 2

Explanation:

$\maltese \: \bf \large \underline \pink{Answer :-}$

We need to know before going to question:

• In the question, they given that, it is a concave mirror.

What is sign convention :

It is a convention which fixes the sign of different distance measured . The sign convention to be formed is new cartesian sign convention it gives the following rules .

• The principal axis of the lens is taken along the x axis of a rectangular coordinate system and optical centre of the lens is taken as the origin.
• All distances are measured from the optical surfaces of the lens
• The distance measured in the same direction as the direction of incident light are taken as positive.
• If the distance measured in the direction opposite to the direction of incident light are taken as negative
• Distance measured upward and perpendicular to the principal Axis of taken as positive
• Distance measured downwards and perpendicular to the principal axis is taken as negative

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Mirror Formula :

${ \tt {\boxed{ \red{ \tt{ \frac{1}{f} \: = \frac{1}{v} + \frac{1}{u} }}}}}$

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Given :

• Object distance (u) = 10cm . By sign convention it is -10 cm
• focal length (f) = 20 cm. By sign convention it is -20 cm.

To Find :

• Image distance (v)

Explanation:

By mirror formula.

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

now we need v, so f is going to other side.

$\sf \: \frac{1}{v} \: = \frac{1}{f} - \frac{1}{u}$

$\sf \: \: \frac{1}{v} \: = \frac{1}{ - 20} + \frac{1}{10}$

$\sf \: \frac{1}{v} \: = \frac{ - 1 + 2}{20}$

$\sf \: \frac{1}{v} \: = \frac{1}{20}$

v = 20 cm

•°• Image distance (v) = +20 cm.