Question

calculate the focal length of a spherical mirror that forms 3 times magnified real image of an object placed 16cm in front of it.diagram also.​

Answer 1

The focal length of the spherical mirror is 12 cm.

Explanation:

Object distance form a mirror, u = -16 cm

It is mentioned that a spherical mirror that forms 3 times magnified real image of an object, m = -3

$m=\dfrac{-v}{u}\\\\-3=\dfrac{-v}{16}\\\\v=48\ cm$

Let f is the focal length of the mirror. Using mirrors formula to find it as :

$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}\\\\\dfrac{1}{48}-\dfrac{1}{(-16)}=\dfrac{1}{f}\\\\f=12\ cm$

So, the focal length of the spherical mirror is 12 cm. Hence, this is the required solution.

Learn more,

Mirrors formula

https://brainly.in/question/3135014

Answer 2

ANSWER:

The focal length of the spherical mirror is 12 cm.

Explanation:

$m=\frac{-v}{u} \\m=3\\u=-16\\mu=-v\\-v=3*(-16)\\v=48$

$\frac{1}{v} -\frac{1}{u} =\frac{1}{f} \\v=48\\u=-16\\\frac{1}{v}=\frac{1}{48}\\\frac{1}{u}=\frac{1}{-16}\\\frac{1}{v} -\frac{1}{u} =\frac{1}{f} \\\frac{1}{48}-\frac{1}{-16}=\frac{1}{f} \\\frac{1}{48}+\frac{1}{16}=\frac{1}{f} \\\frac{1}{f} =\frac{1+3}{48} \\\frac{1}{f} =\frac{4}{48} \\\frac{1}{f} =\frac{1}{12}$

hence The focal length of the spherical mirror is 12 cm.

#SPJ2