Question

an object is placed at a distance of 30 cm from a concave mirror of focal length 20 cm . find the image distance and maginification . also draw the ray diagram​

Answer 1

Given:

$\sf{u=-30cm}$

$\sf{f=-20cm}$

$\sf{Mirror=Concave}$

To Find:

$\sf{1.Image \:Distance(v)}$

$\sf{2.Magnification(m)}$

Solution:

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

$\sf{-{\dfrac{1}{20}}={\dfrac{1}{v}}-{\dfrac{1}{30}}}$

$\sf{{\dfrac{1}{v}}=-{\dfrac{1}{20}}+{\dfrac{1}{30}}}$

$\sf{{\dfrac{1}{v}}={\dfrac{-3+2}{60}}}$

$\sf{{\dfrac{1}{v}}=-{\dfrac{1}{60}}}$

$\sf{v=-60cm}$

Magnification:

$\sf{m=}{\dfrac{-v}{u}}$

$\sf{m=-}{\dfrac{-60}{-30}}$

$\sf{Magnification=-2}$

Therefore, the image will form at 60 cm to the left of the mirror and the image will be real and inverted and twice the size of object.