A student wants to project the image of a candle flame on a screen 48 cm in front of a mirror by keeping the flame at a distance of 12 cm from the pole of the mirror.
(a) Suggest the type of mirror he should use.
(b) Find the linear magnification of the image produced.
(c ) How far is the image from the object ?
(d) Find the focal length of the mirror.
(e ) Draw a ray diagram to show the image formation in this case.

Explanation

(a) Concave mirror as only concave mirror can produce real images.
(b) `u=-12 cm " " v=-48 cm`
`m=-(v)/(u)`
Linear magnification `m=-((-48)/(-12))=-4`
The minus indicates that the image is diminished and real and inverted image.
(c ) Distance of the candle from the screen `= 48-12=36 cm`
(d) `(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/((-48))+(1)/((-12))=(1)/(f), f=-(48)/(5)=-9.6 cm`
This shows that the object is placed between the C and F of the concave mirror.
(e )