Question

a concave mirror produce three times magnified real image of an object placed at 20 cm in front of it . where is the image formed?​

Answer 1

Solution :-

As per the given data ,

• hi = - 3ho ( real , inverted)
• object distance (u) = - 20 cm ( distances are always measured from the pole )

Magnification ,

$\dag \boxed{\mathtt{m = - \dfrac{v}{u}= \dfrac{h_i}{h_o}}}$

here ,

• m = magnification
• v = image distance
• u = object distance
• hi = height of image
• ho = height of object

Hence ,

$\implies \mathtt{-\dfrac{v}{u} = \dfrac{h_i}{h_o}}$

$\implies \mathtt{ v= - \dfrac{h_i \times u}{h_o}}$

$\implies \mathtt{ v= - \dfrac{3h_o \times u}{h_o}}$

$\implies \mathtt{ v= - 3 u }$

$\implies \mathtt{ v= - 3\: x -20 }$

$\implies \mathtt{ v= 60 cm }$

The image is formed at a distance of 60 cm behind the mirror

Extra Information :-

• The focal length of concave mirror is negative
• The focal length of convex mirror is positive

• The focal length of concave lens is negative
• The focal length of convex lens is positive