The image of an object formed by a mirror is real, inverted and is of magnification -1. If the image is at a distance of 40 cm from the mirror, where is the object placed? Where would the image be if the object is moved 20 cm towards the mirror? State reason and also draw ray diagram for the new position of the object to justify your answer.?

Question

Answer

Given Information:

Image formed by mirror is real, inverted and of magnification -1.

Distance of image from mirror is 40 cm.

Finding Object Distance:

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

Using mirror formula, 1/v + 1/u = 1/f where f is the focal length of the mirror.

As the image is real and inverted, v is negative.

Also, magnification = -v/u = -1.

Therefore, -(-u)/u = -1, which gives u = -v = -40 cm.

So, the object is placed at a distance of 40 cm from the mirror.

Finding New Image Position:

If the object is moved 20 cm towards the mirror, its new distance from the mirror would be u' = u - 20 = -60 cm.

Using mirror formula, 1/v' + 1/u' = 1/f

As the magnification remains the same, v' = -u.

Substituting values, we get 1/(-u) + 1/(-60) = 1/f

Solving this equation, we get f = -30 cm.

Using mirror formula again, we can find the new image distance:

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

1/v' + 1/(-60) = 1/-30

1/v' = 1/-30 + 1/60 = 0

Therefore, v' is at infinity, which means the image is formed at the focus of the mirror.

Ray Diagram:

When the object is at a distance of 40 cm from the mirror:

A ray of light from the object parallel to the principal axis gets reflected back and passes through the focus.

A ray of light from the object passing through the focus gets reflected back parallel to the principal axis.

The intersection of these two reflected rays gives the real inverted image of the object.

When the object is moved 20 cm towards the mirror:

The new object is closer to the mirror, so the reflected rays will be more divergent.

The new image will be at the focus of the mirror.

The ray diagram for this situation will have the same two reflected rays, but they will appear more divergent than before.

Similar Class 10 Doubts

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 30 cm from the mirror where is the object placed find the position of the image if the object is no more 20cm towards the mirror.what is the nature of image obtained ?

Q.The linear magnification produced by a spherical mirror is 1/3. Analyzing this value, state the:(i) Type of mirror(ii) Position of the object with respect to the pole of the mirror. Draw a ray diagram to justify your answer.?

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