Question

The image of an object formed by a mirror is real inverted and is of magnification -1 if the image is at the distance of 30cm from the mirror where is the object placed? Find the position of the image obtained? Justify your answer with a ray diagram

Answer 1

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How to determine the position of the image of an object point?

To determine the position of the image, two equations are generally used:

The Newtonian Image Equation describes the position of the bject and the image relative to the focal points of the lens.

The Gauss-equation describes the positions of the object and the image relative to the principal points.

The lens equation.

the magnification is -1  means the image is real and inverted and is of the same size as that of the object.

so if the image is at a distance of 40cm from the mirror then the object is also at a distance of 40cm from the mirror (because the object is placed at C ie center of curvature of the mirror.

if the object is moved 20cm towards the mirror the object is placed at F ie at the principal focus and the image is formed at infinity.

the nature of the mage so formed is real inverted and highly enlarged.

(NOTE draw the ray diagran for an object placed at F for a concave mirror)

Answer 2

Answer:

+ 30 cm

Explanation:

Given :

Magnification = - 1

Image distance = 30 cm

We know

m = - v / u

- 1 = 30 / u

u = - 30 cm

Now we have ,

1 / f = 1 / v + 1 / u

1 /  f = 1 / - 30 - 1 / 30

f = - 15 cm

When object moved 20 cm

u' = - 30 + 20 = - 10 cm

We have f = - 15 cm

We have to find new image distance v'

Again ,

1 / f = 1 / v' + 1 / u'

- 1 / 15 = 1 / v' - 1 / 10

1 / v' = 1 / 30

v' = 30.

Nature of image as :

Virtual

Erect

Magnified.