Question

An object is kept at 50 cm from a concave mirror of radius of curvature 60 cm. Find the image distance. *

-70 cm

75 cm

80cm

-75 cm​

Answer 1

Given:-

→ Distance of the object = 50 cm

→ Radius of curvature = 60 cm

To find:-

→ Distance of image from the mirror.

Solution:-

Firstly, let's calculate focal length of the mirror.

⇒ f = R/2

⇒ f = 60/2

⇒ f = 30 cm

________________________________

Since the mirror is concave, so :-

• u = -50 cm

• f = -30 cm

Now according to mirror formula, we have :-

1/v + 1/u = 1/f

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/(-30) - 1/(-50)

⇒ 1/v = (-1/30) - (-1/50)

⇒ 1/v = [-5 + 3]/150

⇒ 1/v = -2/150

⇒ -2v = 150

⇒ v = 150/-2

⇒ v = -75 cm

Thus, distance of image from the mirror is -75 cm [formed in front of the mirror].

Answer 2

Answer:

Given :-

• An object is kept at 50 cm from a concave mirror of radius of curvature 60 cm.

To Find :-

• What is the image distance.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Focal\: Length\: (f) =\: \dfrac{Radius\: (R)}{2}}}}$

$\longmapsto \sf\boxed{\bold{\pink{\dfrac{1}{v} =\: \dfrac{1}{f} -\: \dfrac{1}{u}}}}$

where,

• v = Image Distance
• u = Object Distance
• f = Focal Length

Solution :-

First, we have to find the focal length :-

Given :

• Radius (R) = 60 cm

According to the question by using the formula we get,

$\implies \sf Focal\: Length =\: \dfrac{\cancel{60}}{\cancel{2}}$

$\implies \sf\bold{\green{Focal\: Length =\: 30\: cm}}$

Now, we have to find the image distance :

As, it is a concave mirror then :

Given :

• Object Distance (u) = - 50 cm
• Focal Length (f) = - 30 cm

According to the question by using the formula we get,

$\implies \sf \dfrac{1}{v} =\: \dfrac{1}{(- 30)} -\ \dfrac{1}{(- 50)}$

$\implies \sf \dfrac{1}{v} =\: \dfrac{- 5 + 3}{150}$

$\implies \sf \dfrac{1}{v} =\: \dfrac{- 2}{150}$

By doing cross multiplication we get :

$\implies \sf (- 2)v =\: 150$

$\implies \sf - 2v =\: 150$

$\implies \sf v =\: \dfrac{\cancel{150}}{\cancel{- 2}}$

$\implies \sf\bold{\red{v =\: -\: 75\: cm}}$

$\therefore$ The image distance is - 75 cm .

Hence, the correct options is option no (4) - 75 cm .