Question

A quarter is resting 18 cm from a concave mirror with a focal length of 6 cm. Calculate the distance from the lens where the image will form.

Answer 1

Using lens formula for concave mirror

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

Here,

u=object distance = -18 cm

f= focal length = - 6cm

v= image distance =?

Now ,

$\begin{gathered} \frac{1}{-6}=\frac{1}{-18}+\frac{1}{v}; \\ \therefore\frac{1}{v}=\text{ }\frac{1}{18}\text{ -}\frac{1}{6}=\text{ -}\frac{1}{9}; \\ \therefore v=\text{ -9} \end{gathered}$

Final Answer is : - 9 cm

Q2) Here,

f= focal length = - 16 cm;

u= object distance = - 44cm

v= image distance = ?

Using mirror formula

$\begin{gathered} \frac{1}{-16}=\text{ }\frac{1}{-44}\text{ +}\frac{1}{v} \\ \frac{1}{v}=\frac{1}{44}-\frac{1}{16}=\text{ }\frac{4-11}{176}=\frac{-7}{176} \\ v=-\text{ }\frac{176}{7}=\text{ -25.14 cm} \end{gathered}$

Answer is -25.14 cm

Q3) Here,

f= -18cm

u=-36 cm

v=?

Using mirror formula

$\begin{gathered} \frac{1}{-18}=\text{ }\frac{1}{-36}+\frac{1}{v} \\ \therefore\frac{1}{v}=\text{ }\frac{1}{36}\text{ -}\frac{1}{18}=\text{ - }\frac{1}{36} \\ v=\text{ -36 cm} \end{gathered}$

Answer is - 36 cm