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Question

(a) Draw a ray diagram to show image formation when the concave mirror produces a real, inverted and magnified image of the object.
(b) Obtain the mirror formula and write the expression for the linear magnification.
(c) Explain two advantages of a reflecting telescope over a refracting telescope.

Solution
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(b) The figure shows an object AB at a distance u from the pole of a concave mirror. The image A1B1 is formed at a distance v from the mirror. The position of the image is obtained by drawing a ray diagram.
Consider the ΔA1CB1 and ΔACB
A1CB1=ACB (vertically opposite angles)
AB1C=ABC (right angles)
B1A1C=BAC (third angle will also become equal)
ΔA1CB1 and ΔACB are similar
ABA1B1=BCB1C
Similarly ΔFB1A1 and ΔFED are similar
EDA1B1=EFFB1
But ED=AB
ABA1B1=EFFB1
If D is very close to P then EF = PF
BCB1C=PFFB1
BC=PCPB
B1C=PB1PC
FB1=PB1PF
PCPBPB1PC=PFPB1PF
But PC=R,PB=u,PB1=v,PF=f
Using sign convention,
PC=R,PB=u,PF=fandPB1=v
So we can equation (3) as :
R(u)v(R)=fv(f)
R+uv+R=fv+f
uRRv=fvf
uvufRv+Rf=Rfvf
uvufRv=RfRfvf
uvufRv=vf
uvuf2fv=vf (R = 2f)
uvuf=2fvfv
uvuf=fv
Dividing throughout by uvf, we will get :
1f1v=1u
1f=1v+1u
This is the required equation.

(c) (i) Reflecting telescopes do not suffer from chromatic aberration.
(ii) Reflecting telescope are cheaper to make than refracting telescopes of the same size

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