A Point source is at a distance of 35 cm on the optical axis from a spherical concave mirror having a focal length 25 cm. At what distance measured along the optical axis from the concave mirror should a plane mirror (perpendicular to principal axis) be placed for the image it forms (due to rays falling on it after reflection from the concave mirror) to coincide with the point source?

Question

Answer

Problem Statement:

A point source is at a distance of 35 cm on the optical axis from a spherical concave mirror having a focal length 25 cm. At what distance measured along the optical axis from the concave mirror should a plane mirror (perpendicular to principal axis) be placed for the image it forms (due to rays falling on it after reflection from the concave mirror) to coincide with the point source? Explain in details.

Solution:

Given:

Distance of point source from concave mirror, u = -35 cm

Focal length of concave mirror, f = -25 cm

As the point source is placed beyond the focal length of the concave mirror, the image formed will be real, inverted and diminished.

Let v be the distance of the plane mirror from the concave mirror.

The image formed by the concave mirror will act as an object for the plane mirror.

Let the image formed by the concave mirror be A'B' and the final image formed by the plane mirror be AB.

Using mirror formula for concave mirror:

1/f = 1/v + 1/u

Substituting the given values, we get:

1/-25 = 1/v + 1/-35

On solving, we get:

v = -87.5 cm

As the image formed is real and inverted, the plane mirror should be placed on the same side of the concave mirror as the object, i.e., to the left of the concave mirror.

Let the distance between the concave mirror and the plane mirror be x.

Using similar triangles, we can say:

(x + v)/x = AB/A'B'

As the final image coincides with the point source, AB = u = -35 cm

Also, as the concave mirror is spherical, we need to take into account the spherical aberration.

Let the height of the point source be h.

Using spherical aberration formula, we can say:

h/AB = 2(f + v)/(f - v)

Substituting the given values, we get:

h/-35 = 2(-25 - 87.5)/(-25 + 87.5)

On solving, we get:

h = -12.5 cm

Therefore, the distance of the plane mirror from the concave mirror should be:

x = (AB * v)/(AB - A'B')

Substituting the given values, we get:

x = (-35 * -87.5)/(-35 - (-12.5))

On solving, we get:

x = -70 cm

Answer:

The plane mirror should be placed at a distance of 70 cm from the concave mirror measured along the optical axis.

Answer

Answer is 61.25 cm

https://edurev.in/studytube/Answer-is-61-25-cm/062395db-5e8d-4198-8944-87a9d10e72df_t?courseId=-1

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