Question

Find the image distance from a concave mirror of focal length 10 cm if object is placed at a distance of 20 cm from it.
O 10 cm O 30 cm o 20 cm O 40 cm​

Answer 1

AnswEr :

As per the provided information in the given question, it has been stated that the the focal length of the concave mirror is 10 cm and the object is placed at a distance of 20 cm from it. We've been asked to calculate the image distance from the concave mirror.

The focal length of a concave mirror is negative because the focus of concave mirror is in the front of the mirror (in the left side). Thus, the focal length will be –10 cm. And, as the object is always placed is placed to the left side of the mirror, so object distance will also be negative. Thus, object distance will be –20 cm.

We have,

• Object distance, u = –20 cm
• Focal length, f = –10 cm

$\longrightarrow$ Image distance, v = ?

By using the mirror formula,

$\longrightarrow \boxed{\tt { \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} } }$

• f denotes focal length
• v denotes image distance
• u denotes object distance

$\longrightarrow \tt { \dfrac{1}{-10} = \dfrac{1}{v} + \dfrac{1}{-20} }\\ \\ \longrightarrow \tt {- \dfrac{1}{10} = \dfrac{1}{v} - \dfrac{1}{20} }\\ \\ \longrightarrow \tt {- \dfrac{1}{10} + \dfrac{1}{20}= \dfrac{1}{v} }\\ \\ \longrightarrow \tt {\dfrac{-2 + 1}{20}= \dfrac{1}{v} }\\ \\ \longrightarrow \tt {\dfrac{-1}{20}= \dfrac{1}{v} } \\ \\ \longrightarrow \underline{ \boxed{\tt {-20 \; cm = v}} }\; \red{\bigstar}$

Therefore, the image distance from a concave mirror is 20 cm. The negative sign denotes that it is formed in the front of the mirror or left side of the mirror.

(Option C)

Answer 2

Given:

An object is placed at a distance of 20 cm from a concave mirror of focal length 10 cm.

To find:

Image distance?

Calculation:

Applying Mirror Formula:

$\rm \: \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

$\rm \implies \: \dfrac{1}{( - 10)} = \dfrac{1}{v} + \dfrac{1}{( - 20)}$

$\rm \implies \: - \dfrac{1}{ 10} = \dfrac{1}{v} - \dfrac{1}{20}$

$\rm \implies \: \dfrac{1}{v} = - \dfrac{1}{10} + \dfrac{1}{20}$

$\rm \implies \: \dfrac{1}{v} = \dfrac{ - 2 + 1}{20}$

$\rm \implies \: \dfrac{1}{v} = \dfrac{ - 1}{20}$

$\rm \implies \: v = - 20 \: cm$

So, image distance is 20 cm in front of mirror.