Question

a 2.5cm high object is placed 7.10cm from a concave mirror whose radius of curvature is 10.20cm. find the location of the image and it's size.

Answer 1

refer the pic for answer

Answer 2

Given,

The distance of the object from the mirror, u = + 7.10 cm

The radius of curvature of the mirror, R = + 10.20 cm (concave mirror)

To find,

The location and size of the image.

Solution,

In order to solve this question correctly and quickly, we can follow the given steps.

From what knowledge we have of this chapter in Physics we know that,

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

But the focal length of the mirror is not given but the radius of curvature is and we are aware that,

f = $\frac{R}{2}$

= $\frac{10.2}{2}$

= 5.1 cm

So, the focal length was calculated to be 20.4 cm.

Now in order to calculate the distance of the image let us rearrange the equation above,

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

= $\frac{1}{5.1} -\frac{1}{7.1}$

= $\frac{2}{36.21}$

= $\frac{1}{18.1}$

Thus, the distance of the image was calculated to be 18.1 cm away.

Now, in order to calculate the size. We have to calculate to magnification,

Magnification, m = $\frac{-v}{u}$

= $\frac{18.1}{7.1}$

= 2.5

Another equation of magnification we have is,

m = $\frac{h'}{h}$

Where,

h' = the size of the image

h = the size of the object

If we rearrange the equation above we will be able to calculate the size of the image,

h' = $\frac{m}{h}$

= $\frac{2.5}{2.5}$

= 1 cm

Hence, the distance of the image formed is 20.4 cm and the height of the image is 1 cm.