Question

Derive a relationship between the focal length and radius of curvature of a spherical mirror. (Grade 12 NCERT )​ Please don't answer from GOOGLE. ..

Answer 1

Answer:Focal length f = Radius of curvature R/2

Hope it will help you!

Have a great day

Answer 2

MPN= Concave spherical mirror

P=Pole

F= Principle focus

C=Centre of curvature

PC=Principle axis

f= Focal length of mirror

R= Radius of curvature of mirror

AD= incident ray

EF=reflected ray

DC= Normal at point D

Angle of incidence=∠ADC

Angle of reflection=∠CDF

∠ADC=∠ CDF=θ(let)(By second law of reflection)

∠ADC=∠DCF=θ(alternate angles)

In ΔDCF,

∠CDF=∠DCF

ΔDCF is a isocsleles triangle

∴DF=PC [sides opp. toequal.

angles in a triangle are

equal]

If the aperture of mirror is very small i.e., point D is very near to point P then.

DF=PF(approx)

Hence, PF=FC

PE+PF=PF+FC

2PF=PC ...(i)

Applying sign convention,

PF=−f,PF=R

Put in eq. (1)

2(−f)=−R

R=2f

HOPE THIS WILL HELP YOU FRIEND!!☺️☺️