A mirror produces two times enlarged image behind it when an object is placed at some distance from it. If the focal length of the mirror is 10 cm . Calculate position of the object and position of the image?

Question

Answer

Explanation:

When an object is placed at some distance from a mirror, it produces an image due to the reflection of light. In this case, the mirror is producing a two times enlarged image, which means that the height of the image is twice the height of the object. The focal length of the mirror is given as 10 cm. We need to calculate the position of the object and the position of the image.

Formula:

The formula for calculating the position of the object and the position of the image is given by:

1/f = 1/u + 1/v

Where,

f = focal length of the mirror

u = distance of the object from the mirror

v = distance of the image from the mirror

Calculation:

Given,

f = 10 cm

m = 2 (as the image is two times enlarged)

Let the distance of the object from the mirror be u.

Using the mirror formula, we can write:

1/10 = 1/u + 1/v

As the image is two times enlarged, we can write:

m = v/u = 2

Substituting the value of v/u in the above equation, we get:

1/10 = 1/u + 1/2u

On solving the above equation, we get:

u = 20 cm

Substituting the value of u in the equation v/u = 2, we get:

v = 40 cm

Position of the Object and Image:

The distance of the object from the mirror is 20 cm.

The distance of the image from the mirror is 40 cm.

Therefore, the object is placed at a distance of 20 cm from the mirror and the image is formed at a distance of 40 cm from the mirror. The image is two times enlarged compared to the object.

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