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

`(1)/(f)=(1)/(u)+(1)/(v);`

Here,

u=object distance = -18 cm

f= focal length = - 6cm

v= image distance =?

Now ,

`\begin{gathered} (1)/(-6)=(1)/(-18)+(1)/(v); \\ \therefore(1)/(v)=\text{ }(1)/(18)\text{ -}(1)/(6)=\text{ -}(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} (1)/(-16)=\text{ }(1)/(-44)\text{ +}(1)/(v) \\ (1)/(v)=(1)/(44)-(1)/(16)=\text{ }(4-11)/(176)=(-7)/(176) \\ v=-\text{ }(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} (1)/(-18)=\text{ }(1)/(-36)+(1)/(v) \\ \therefore(1)/(v)=\text{ }(1)/(36)\text{ -}(1)/(18)=\text{ - }(1)/(36) \\ v=\text{ -36 cm} \end{gathered}`

Answer is - 36 cm