Question

a candle of height 5 cm placed 60 cm from concave mirror with focal length 40 cm find image distance and image height​

Answer 1

Here using mirror formula

1/f=1/u+1/v

1/-40=1/-60+1/v

1/v=40-60/240

1/v= -20/240

1/v=-1/12

v=-12cm

m=-v/u

=12/60

=1/5

m=h'/h

1/5=h'/5

h'=1cm

Answer 2

Given:
Object Height (h) = 5cm
Object distance (u) = 60cm (concave mirror)
Focal length(f)= 40cm

To find:
Image distance (v)= ?
Image Height (h¹)= ?

$\underline{Using\: Mirror\: Formula}$

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

=> $\dfrac{1}{v}$ = $\dfrac{1}{40}$ - $\dfrac{1}{60}$

=> $\dfrac{1}{v}$ = $\dfrac{40+60}{40×60}$

=> $\dfrac{1}{v}$=$\dfrac{100}{2400}$

=> $\boxed{v= 24cm}$

$\underline{Magnification\: Formula}$

m = $\dfrac{h^1}{h}$ = $\dfrac{-v}{u}$

m = $\dfrac{h^1}{5}$ = $\dfrac{-24}{60}$

m = 60h¹ = -24(5)

m = 60h¹= -120

m = h¹= $\dfrac{-120}{60}$

Therefore $\boxed{ h^1 = -2}$