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CBSE Class 10 Answered

Prove that 1.sini=sine 2.R=2f 3.1/f=1/v-1/u 4.1/f=1/v+1/u
Asked by Debdulal | 12 Sep, 2018, 11:02: AM
Multiple questions are not allowed in one posting. We answer only one question per posting.
Hence I am answering to the question, Prove that R = 2f .
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This question " prove that R = 2f " is related to reflection in spherical mirrors.
Let us consider a parallel ray incident on point M of concave mirror as shown in figure.
After reflection it is passing through the focal point F. Let MC is radius of curvature.
Then CM is normal to the mirror. If the incident ray makes angle θ with CM, then angle CMF is also θ, due to law of reflection.

Let us draw a perpendicular from M to principle axis of mirror and let this perpendicular line meet the principle axis at D.

Since the incident ray is parallel to principle axis, angle MCF = θ.  hence angle MFD = 2θ.

from ΔMCD and ΔMFD, we write,    tanθ = MD / CD  ..................(1)
tan(2θ) = MD / FD ..................(2)

if the incident ray is very close to principle axis, angle θ and angle 2θ are very small. in that case tanθ ≈ θ and tan(2θ) ≈ 2θ

hence we rewrite eqns.(1) and (2) as,  θ   = MD / CD ...............(3)
2θ = MD / FD ...............(4)
from (3) and (4), we have CD = 2×FD ............(5)

again when incident ray is very close to principle axis, points D and P merge together.

Hence we write CP = FP or R = 2F

R is radius of curvature of concave mirror and F is its Focal length
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