Question

When a bright object is placed 10 CM away from a concave mirror, it's real image is formed at a distance 40 CM from the mirror. What is the focal length of the mirror?

Answer 1

• object distance=u=-10cm
• image distance=v=40cm
• Focal length=f=?

Using mirror formula

$\boxed{\sf \dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}}$

$\\ \sf\longmapsto \dfrac{1}{40}-\dfrac{1}{-10}=\dfrac{1}{f}$

$\\ \sf\longmapsto \dfrac{1}{f}=\dfrac{1}{40}+\dfrac{1}{10}$

$\\ \sf\longmapsto \dfrac{1}{f}=\dfrac{1+4}{40}$

$\\ \sf\longmapsto \dfrac{1}{f}=\dfrac{5}{40}$

$\\ \sf\longmapsto f=\dfrac{40}{5}$

$\\ \sf\longmapsto f=8cm$

Answer 2

${\huge{\underline{\large{\mathbb{ \green{VERIFIED \: ANSWER}}}}}}$

1/u +1/v = 1/f

1 /-10 +1 /40 = 1/f

-1/10 +1/40= 1/f

-4/40 +1/40 =1/f

-4+1/40 = 1/f

-3/40 =1/f

40/-3=f

f=13.3333