Question

an object is placed 10 cm from a concave mirror the focal length is 5 cm. Determine
a) Image distance
b) Magnification of image​

Answer 1

Answer:

• Image distance is -10 cm
• Magnification of image is -1

Given:

• Object distance (u) = -10 cm [Object is on the left side of the mirror that is -ve side].
• Focal length (f) = -5 cm [Focus of the concave mirror is in the front of the mirror, on the left side].

Explanation:

$\rule{300}{1.5}$

From mirror formula we know,

$\bigstar\ {\underline{\boxed{\sf{\dfrac{1}{v}\ +\ \dfrac{1}{u}\ =\ \dfrac{1}{f}}}}}$

This implies the relationship between the focal length, the distance of the object from the mirror, and the distance of the image from the mirror.

Here,

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

Substitute the respective values,

${\longrightarrow{\sf{\dfrac{1}{v}\ +\ \dfrac{1}{u}\ =\ \dfrac{1}{f}}}} \\ \\ \\ {\longrightarrow{\sf{\dfrac{1}{v}\ +\ \dfrac{1}{-10}\ =\ \dfrac{1}{-5}}}} \\ \\ \\ {\longrightarrow{\sf{\dfrac{1}{v}\ -\ \dfrac{1}{10}\ =\ \dfrac{1}{-5}}}} \\ \\ \\ {\longrightarrow{\sf{\dfrac{1}{v}\ =\ \dfrac{1}{-5}\ +\ \dfrac{1}{10}}}} \\ \\ \\ {\longrightarrow{\sf{\dfrac{1}{v}\ =\ \dfrac{-2\ +\ 1}{10}}}} \\ \\ \\ {\longrightarrow{\sf{\dfrac{1}{v}\ =\ \dfrac{-1}{10}}}} \\ \\ \\ {\longrightarrow{\large{\underline{\boxed{\red{\sf{v\ =\ -10\ cm}}}}}}}$

∴ The image distance is -10 cm.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Now, let us find out the magnification of the image.

From magnification formula we know,

$\bigstar\ {\underline{\boxed{\sf{m\ =\ \dfrac{-v}{u}}}}}$

Here,

• m denotes magnification.
• v denotes image distance.
• u denotes object distance.

Substitute the respective values,

${\longrightarrow{\sf{m\ =\ \dfrac{-v}{u}}}} \\ \\ \\ {\longrightarrow{\sf{m\ =\ \dfrac{-(-10)}{-10}}}} \\ \\ \\ {\longrightarrow{\sf{m\ =\ \dfrac{-10}{10}}}} \\ \\ \\ {\longrightarrow{\large{\underline{\boxed{\red{\sf{m\ =\ -1}}}}}}}$

∴ The magnification of the image is -1.

$\rule{300}{1.5}$