Question

An object is placed 50cm infront of a convex mirror of radius of curvature 100cm . The magnificention will be

Answer 1

Answer :

Given -

• Convex mirror
• The object distance is - 50 cm
• The radius of curvature is + 100 cm

To Find -

• Magnification ?

Solution -

Radius of curvature of the convex mirror is 100 cm.

So, the focal length of the convex mirror will be 50 cm.

We also know about the object distance which is - 50 cm.

Hence, by using the mirror formula :

⇒ 1/v + 1/u = 1/f

⇒ 1/v + 1/-50 = 1/50

⇒ 1/v = 1/50 + 1/50

⇒ 1/v = 2/50

⇒ 2v = 50

⇒ v = 50/2

⇒ v = 25 cm

Hence, the image distance is 25 cm.

Now, the formula for magnification is -v/u.

Hence, Magnification = -25/-50

➜ Magnification = 1/2 = 0.5

Answer 2

Given :

• Object Distance (u) = - 50 cm
• Radius of Curvature (R) = 100 cm
• Convex mirror

To Find :

• Magnification of the mirror

Solution :

As we know that,

➠ R = 2f

⇒100 = 2f

⇒f = 100/2

⇒f = 50

$\therefore$ Focal length of convex mirror is 50 cm

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Now, we have to find out image distance from mirror formula :

⇒1/f = 1/v + 1/u

⇒1/50 = 1/v + (-1/50)

⇒1/50 = 1/v - 1/50

⇒1/v = 1/50 + 1/50

⇒1/v = 2/50

⇒v = 25

$\therefore$ Image distance is 25 cm from mirror

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Now, use formula for magnification :

⇒m = -v/u

⇒m = -25/-50

⇒ m = 25/50

⇒m = 1/2

⇒m = 0.5

$\therefore$ Magnification of Image is 0.5