Home
Class 12
PHYSICS
Derive spherical mirror formula (1)/(v) ...

Derive spherical mirror formula `(1)/(v) + (1)/(u) = (1)/(f)`, where all the symbols have their usual meaning.

Text Solution

Verified by Experts


In above figure, triangles A. B. F and ENF are similar,
So, `(A.B.)/(NE) = (A.F)/(NF)`
Since, the aperture of concave mirror is small, therefore, NF = PF and NF = AB.
So, `(A.B.)/(AB) = (A.F)/(PF)`
As, `A.F = PA. - PF`
`therefore (A.B.)/(AB) = (PA. -PF)/(PF)` ....(i)
Also, `(A.B.)/(AB) = (PA.)/(PA)` ...(ii)
[`therefore` Traingles ABP and A.B.P are similar]
From Eqs. (i) and (ii), we get
`(PA.-PF)/(PF) = (PA.)/(PA)` ...(iii)
Using sign convention,PA = - u, PA. = - v and PF = - f Substituting values in Eq. (iii), we get
`(-v-(-f))/(-f) = (-v)/(-u)`
`(-v+f)/(-f) = (v)/(u) rArr (v)/(f) - 1 = (v)/(u)`
Dividing both sides by v, we get
`(1)/(f) = (1)/(v) + (1)/(u)`
This is the mirror formula for spherical mirror.
Promotional Banner

Similar Questions

Explore conceptually related problems

From Arrhenius equation derive the relation log((k_2)/(k_1))=(Ea)/(2.303R)((T_2-T_1)/(T_1 T_2)) where the symbols have their usual meanings.

Establish the relation C_p - C_v = R where the symbols have their useful meanings.

Establish a relation between B, H and I where the symbols carry their usual meanings.

The linear magnification in case of spherical mirror (where the symbols carry their usual meanings) is