Question

a mirror forms an image which is 30 cm from the object and twice its height​ where must the mirror be situated what is the radius of curvature is the mirror concave or convex
quality answer needed​

Answer 1

Answer:

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Answer 2

Answer:

• The mirror is situated at a distance of 10 cm from the object.
• The radius of curvature = -40 cm
• Concave mirror

Explanation:

A mirror forms an image which is 30 cm from the object and twice its height.

=> The distance between the object and the image is 30 cm

   v - u = 30 cm ➜ (eqn. 1)

=> height of the image = 2 × height of the object

     $\longrightarrow \sf h_i=2h_o \\\\ \longrightarrow \sf \dfrac{h_i}{h_o}=2$

 The magnification is the ratio of the size of the image to that of the object.

 $\longmapsto \sf m=\dfrac{-v}{u}=\dfrac{h_i}{h_o}$

    $\implies \tt 2=\dfrac{-v}{u} \\\\ \implies \boxed{\tt v=-2u}$

Substitute v = -2u in equation.1 :

-2u - u = 30

 -3u = 30

  u = 30/-3

  u = -10 cm

The object is placed at 10 cm in front of the mirror.

The mirror is situated at a distance of 10 cm from the object.

_____________________________

⇒ v = -2u

⇒ v = -2(-10)

⇒ v = 20 cm

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

$\rm \dfrac{1}{f}=\dfrac{1}{20}+\dfrac{1}{-10} \\\\ \rm \dfrac{1}{f}=\dfrac{1}{20}-\dfrac{1}{10} \\\\ \rm \dfrac{1}{f}=\dfrac{1-2}{20} \\\\ \rm \dfrac{1}{f}=\dfrac{-1}{20} \\\\ \rm f=-20 \ cm$

Radius of curvature, R = 2f

R = 2(-20)

R = -40 cm

As the focal length of the mirror is negative, it is a concave mirror.