Question

An object is placed 10 cm from a convex mirror of radius of curvature 60 cm. Find the position of image

Answer 1

Given:

• Object Distance (u) = -10cm
• Radius of curvature (R) = 60cm

To Find:

• Position of Image?

Formula Used:

$\\ \bigstar{\underline{\boxed{\sf\green{ Mirror \ Formula = \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }}}} \\ \\ \bigstar{\underline{\boxed{\sf\green{ Focal \ length (f) = \dfrac{R}{2} }}}}$

Solution:

Focal length (f) = R/2 = 60/2 => 30cm

After putting the values in the Mirror Formula;

$\colon\implies{\sf{ \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }} \\ \\ \colon\implies{\sf{ \dfrac{1}{v} = \dfrac{1}{f} - \dfrac{1}{u} }} \\ \\ \colon\implies{\sf{ \dfrac{1}{v} = \dfrac{1}{30} - (- \dfrac{1}{10} ) }} \\ \\ \colon\implies{\sf{ \dfrac{1}{v} = \dfrac{1}{30} + \dfrac{1}{10} }} \\ \\ \colon\implies{\sf{ \dfrac{1}{v} = \dfrac{4}{30} }}$

After Reversing Fraction,

$\colon\implies{\sf{ v = \cancel{ \dfrac{30}{4} } }} \\ \\ \colon\implies{\sf\bold\purple{ v = 7.5 \ cm }}$

Hence,

The Position of an image is 7.5 cm.