Question

radius of curvature of a concave mirror is 40 cm. find position of real image of a object in front of the mirror, so that its magnification -2

Answer 1

Given :

• Radius of Curvature (R) = -40 cm
• Magnification (m) = -2

To find :

• Image position

Solution :

m = -v/u

⇒- 2 = -v/u

⇒2 = v/u

⇒v = 2u

⇒u = v/2.....(1)

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Use Mirror formula

⇒1/f = 1/v + 1/u

⇒1/v = 1/-20 + 2/v

⇒1/v = (-v + 20(2))/20v

⇒1/v = (-v + 40)/20v

⇒20v/v = -v + 40

⇒ 20 = -v + 40

⇒v = 40 - 20

⇒v = 20 cm

$\therefore$ Image is formed at 20 cm from mirror

Answer 2

Answer:

Given –

• Concave mirror.
• Radius of curvature = 40 cm.
• The magnification of the image = -2.

To Find –

• Position of the image.

Solution –

Magnification = -v/u

➸ -v/u = -2

➸ -v = -2u

➸ v = 2u

➸ u = v/2

Mirror Formula : 1/v + 1/u = 1/f

➸ 1/v + 1/-v/2 = 1/-20

➸ 1/v - 2/v = -1/20

➸ 1/v = -1/20 + 2/v

➸ 1/v = (-v + 40)/20v

➸ 20v/v = -v + 40

➸ 20 = -v + 40

➸ -v = 20 - 40

➸ -v = -20

➸ v = 20 cm

Image will be formed 20 cm away from the mirror.