How far should an object be placed from a concave mirror of focal length 20 cm to obtain its image - Science - Light - Reflection and Refraction

Question

How far should an object be placed from a concave mirror of focal
length 20 cm to obtain its image at a distance of 30 cm from the
mirror? What will be the height of the image if the object is 6 cm
tall?

Vipra Mishra · Accepted Answer

Solution
u=?f=-20cmv=- 30 cm   (considering image is virtual) h1=6cm h2=? By Mirror formula, 1/v+1/u=1/f- 1/30+1/u=-1/20 1/u=1/30-1/20 1/u=20-30600 =-10600u= -60 cm  h2/h1=-v/u  h2/h1=--30-60 = -12 h2=-12×6 = -3 cm  u=?f=-20cmv=30 cm   (considering image is real) h1=6cm h2=? By Mirror formula, 1/v+1/u=1/f 1/30+1/u=-1/20 1/u=-1/30-1/20 1/u=-20-30600 =-50600=-112u= -12 cm  h2/h1=-v/u  h2/h1=--30-12 = -2
5 h2=-2 5×6 = -15 cm

How far should an object be placed from a concave mirror of focal length 20 cm to obtain its image at a distance of 30 cm from the mirror? What will be the height of the image if the object is 6 cm tall?