Question

Consider the situation where:
 An object is 3 cm (height)
 Mirror is concave with 6 cm focal length.
 Object is placed at the centre of curvature.
Which of the following options are correct?
A. The mirror will produce an image of magnification +1.5.
B. The mirror will produce an image of magnification -1.
C. The mirror will produce an image of magnification +1.
D. The mirror will produce an image of magnification -1.5.

Answer 1

Answer:

(B) The mirror will produce an image of magnification - 1.

Explanation:

We know that when an object is kept at centre of curvature of a concave mirror then a real and inverted image of same size  is formed at centre of curvature itself.

So, in this case magnification produced by the mirror is - 1.

Here - (negative sign) represent that image is real and inverted and 1 represent that the height of image is same as the height of the object.

So,

Correct answer : (B) The mirror will produce an image of magnification - 1.  

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Answer 2

Given: An object is 3 cm (height). Mirror is concave with 6 cm focal length. Object is placed at the centre of curvature.

To find: The magnification produced by the mirror.

Solution:

• The centre of curvature of a mirror is twice its focal length. Hence, the position of the object can be calculated as,

        $u = 2 * f$

           $= 12 cm$

• To find the distance of the image from the mirror, the following formula is used.

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

• Here, v is the distance of the image, u is the distance of the object from the mirror and f is the focal length.

       $\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$

          $= \frac{1}{6} - \frac{1}{12}$

          $= \frac{1}{12}$

       $v = 12 cm$

• The linear magnification produced by a spherical lens is the ratio of the size of the image formed by the lens to the size of the object, both measured perpendicular to the principal axis.
• It is given by the formula,

        $m = \frac{v}{u}$

• Here, m is the magnification produced.

        $m = \frac{12}{12}$

            $= 1$

Therefore, the correct option is C. The mirror will produce an image of magnification +1.