Question

Find the focal length of a concave mirror that produces four times larger real image of an object held at 5cm from the mirror.

Answer 1

Answer:

Explanation:

Given,

Image distance, v = 4 times of object

The object held at 5 cm from the mirror .

To Find,

Focal length of the concave mirror.

Formula to be used,

Magnification, m = - v/u = h(i)/h(o)

Mirror formula = 1/f = 1/v + 1/u

Solution,

Putting all the values, we get

Magnification, m = - v/u = h(i)/h(o)

⇒ - v/u = 4

⇒ v/u = - 4

⇒ v = - 4u

⇒ v = - 4 × (- 5)

⇒ v = 20 cm

Here, the object distance is 20 cm.

Now, the focal length of a concave mirror,

1/f = 1/v + 1/u

⇒ 1/f = 1/20 + 1/(- 5)

⇒ 1/f = 1/20 - 1/5

⇒ 1/f = (1 - 4)/20

⇒ 1/f = - 3/20

⇒ 1/f = - 20/3

⇒ f = - 20/3

⇒ f = - 6.67 cm

Hence, the focal length of the concave mirror is 6.67 cm.

Answer 2

Answer:

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