Question

An object of height 6cm is placed on the principal axis of a concave mirror of focal length f at a distance of 4f. Find the height and nature of the image

Answer 1

the image formed is a point image.
It is real, inverted and formed at focus.

Answer 2

Answer:

The image formed is reduced in size and upright in nature.

Explanation:

Step 1 : write down the formula relating the focal length, image distance and the object distance.

Let the image distance be v, the object distance be u and the focal length f then we have :

1/f = 1/u + 1/v

Step 2 : The focal length of a concave mirror is positive.

From the question we have the focal length and the object distance.

We can therefore calculate the image distance.

1/f - 1/4f = 4/4f - 1/4f = 3/4f

= 4/3f

Step 3 : Calculate the magnification.

Magnification = image distance / object distance

= 4/3f ÷ 4f

= 4/3f × 1/4f = 1/3

Magnification = 1/3

Step 4 : From this we can calculate the image height.

Magnification = image height / Object height

1/3 = h/6

h = 6/3 = 2 cm

The nature of the image is :

I) It's reduced in size.

2) It's upright since the magnification is positive.