Question

A convex lens forms an image at a distance of 10 cm when a parallel beam of light is incident on it.Find the positions of a convex mirror of radius of curvature 5 cm such that the final image is formed at infinity

Answer 1

For a convex mirror of radius 5 cm such that the final image is formed at infinity the the distance at which the  object should be placed is 2.5 cm from the convex mirror

Explanation:

• The radius of curvatureof a spherical mirror is always double that of the focus of the the spherical mirror. In the above example we see that the image is formed at infinity. In case of a convex mirror the image is formed at infinity only when the object is placed at the focus of the convex mirror.

• Hence the object should be placed at half the distance of the radius of curvature that is 2.5 cm from the convex mirror

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The image formed by a convex mirror is only one-third of the size of ..

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Answer 2

Given that,

Image distance = 10 cm

Radius of curvature = 5 cm

Image distance = ∞

We need to calculate the focal length

Using formula of radius of curvature

$R=2f$

$f=\dfrac{R}{2}$

Put the value into the formula

$f=\dfrac{5}{2}$

$f=2.5\ cm$

The object distance is equal to the position of convex mirror.

We need to calculate the position of convex mirror

Using formula of mirror

$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$

Put the value into the formula

$\dfrac{1}{2.5}=\dfrac{1}{\infinty}+\dfrac{1}{u}$

$u=2.5\ cm$

Hence, The position of convex mirror is 2.5 cm.