Question

a concave mirror produces a real image 10mm tall,of an object 2.5mm tall placed at 5cm form the mirror. calculate the focal length and position of images

Answer 1

hi=-10 mm
ho=2.5 mm
u=-50 mm or -5 cm
v=?
f=?
m=hi/ho
=-10/2.5
=-4
m=-v/u
-4=-v/-50
v=-(-4*-50)
=-200 mm
=-20 cm
1/f=1/v+1/u
1/f=1/-20+1/-5
=-1/20+-1/5
=-1-4/20
=-5/20
=-1/4

Answer 2

Answer:

The focal length of the concave mirror is 4 cm and the image will be formed at 20 cm and image is real.

Explanation:

Given that,

Height of image h'=10 mm

Height of object h = 2.5 mm

Distance of the object u = 5 cm

Using formula of magnification

$m=\dfrac{-h'}{h}=-\dfrac{v}{u}$

$\dfrac{0.1 cm}{0.25\ cm}=\dfrac{v}{-5}$

$v= -20\ cm$

The distance of the  image is 20 cm.

Using mirror's formula

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

$\dfrac{1}{f}=\dfrac{1}{-20}+\dfrac{1}{-5}$

$\dfrac{1}{f}=\dfrac{-5}{20}$

$\dfrac{1}{f}=\dfrac{-1}{4}$

$f= -4\ cm$

The focal length of the mirror is 4 cm.

Hence, The focal length of the concave mirror is 4 cm and the image will be formed at 20 cm and image is real.