Derive mirror formula for a concave mirror when image formed is (i) real (ii) virtual. Also give the sign convention used.

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Solution

i) When image formed is real

u is –ve

v is –ve

f is –ve

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

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

ii) When image formed is virtual

u is –ve

v is +ve

f is –ve

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

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Derive mirror formula for a concave mirror when image formed is (i) real (ii) virtual. Also give the sign convention used.

i) When image formed is real u is –ve v is –ve f is –ve 1−f = 1−v + 1−u 1f = 1v + 1u ii) When image formed is virtual u is –ve v is +ve f is –ve 1−f = 1v + 1−u

i) When image formed is real

u is –ve

v is –ve

f is –ve

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

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

ii) When image formed is virtual

u is –ve

v is +ve

f is –ve

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