Question

A dentist uses a small concave mirror of focal length of 3 cm and holds it at a distance of 2 cm from the tooth. Which of the following statement is incorrect about the image formed?

a) The image is three times the size of the object.

b) The image distance is 6 cm from the pole.

c) The image formed is erect.

d) The distance between the object and the image is 8 cm.

e) None of the above

• A. The image is three times the size of the object.
• B. The image distance is -6 cm from the pole.
• C. The image formed is erect.
• D. The distance between the object and the image is 8 cm.

Answer 1

Answer: (B)

Step 1: Given that:
The focal length($f$) of the concave mirror used by the dentist = $-3cm$
Object distance($u$) = $-2cm$

(Note; The object distance and the focal length of the concave mirror are taken negative as both are the distances to the left of the pole of the mirror.)

Step 2: Calculation of the image distance:

Using mirror formula:

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

Where, u = Object distance, v= image distance and f= focal length

Putting the values, we get

$\frac{1}{v}+\frac{1}{-2cm}=\frac{1}{-3cm}$

$\frac{1}{v}-\frac{1}{2}=-\frac{1}{3}$

$\frac{1}{v}=\frac{1}{2}-\frac{1}{3}$

$\frac{1}{v}=\frac{3-2}{6}$

$\frac{1}{v}=\frac{1}{6}$

$v=6cm$

Thus, the image distance is 6cm.

Step 3: determination of the size of the image with respect to the size of the object:

Using magnification formula; $m=\frac{h_i}{h_o}=-\frac{v}{u}$

Where $h_i$ = Size of the image

$h_o$ = Size of the object

Putting the values, we get

$\frac{h_i}{h_o}=-\frac{6cm}{-2cm}$

$\frac{h_i}{h_o}=3$

$h_i=3h_o$

Thus, the image is three times the size of the object.

As the magnification is positive the image is virtual and erect.

The distance between the object and image = $u+v$

= 2+6

= 8cm

Thus, Option e) None of the above is the correct option.