Question

A dentist uses a mirror in front of a decayed tooth at a distance of 4 cm from the tooth to get a four times magnified image.
use the mirror formula to find the focal length and nature of mirror used
what is the nature of image

Answer 1

» Given

A dentist uses a mirror in front of a decayed tooth at a distance of 4 cm [means u = 4cm]

from tooth to get a four times magnified image [means h' = 4h]


• Now

u = distance between object and mirror.

v = distance between image and mirror.

f = focal length

So...

$\dfrac{1}{f}$ = $\dfrac{1}{v}$ + $\dfrac{1}{u}$ ....(1)

We also given that

u = - 4 cm [as object is always puts in left side so it's sign is -ve]

h' = 4h

$\dfrac{h'}{h}$ = 4 cm

Now

m = $\dfrac{-v}{u}$

4 = $\dfrac{-v}{-4}$

[As m = $\dfrac{h'}{h}$ = $\dfrac{-v}{u}$]

v = + 16 cm

Put value of v and u in eq. (1)

$\dfrac{1}{f}$ = $\dfrac{1}{16}$ + $\dfrac{1}{-4}$

$\dfrac{1}{f}$ = $\dfrac{1}{16}$ - $\dfrac{1}{4}$

$\dfrac{1}{f}$ = $\dfrac{1\:-\:4}{16}$

$\dfrac{1}{f}$ = $\dfrac{-3}{16}$

f = $\dfrac{-16}{3}$

f = - 5.33 cm

As f = - 5.33 cm

v = + 16 cm

u = - 4 cm

So, it is clear from above that it is a $\textbf{Concave mirror}$. And also known as Converging mirror.

As object is placed between f and P. So, image is formed behind the mirror.

So, it's clear that nature of image is $\textbf{erect and virtual}$. Image formed is $\textbf{enlarged}$.

Answer 2

Answer :

Focal length - $-5.33$ cm

Mirror used - Concave mirror

Nature - Virtual, Erect

Step-by-step explanation :

Given,

Object distance, $u=-4$ cm

Magnification, $m=4$

Since, we know,

⇒ $m=\frac{-u}{v}$

Therefore,

⇒ $v=-mu$

⇒ $v=-(4)\times (-4)$

⇒ $16$ cm

So, image distance, $v=16$ cm

Now, by using mirror formula,

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

⇒ $\frac{1}{16}+\frac{1}{-4}=\frac{1}{f}$

⇒ $\frac{1-4}{16}=\frac{1}{f}$

⇒ $\frac{1}{f}=\frac{-3}{16}$

⇒ $f=-5.33$ cm

The mirror used in this case is concave mirror because magnified images can be made only by concave mirror.

Now, since the image is formed behind the mirror, therefore nature of image is virtual and erect.