(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.
(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=PC−PB
B1C=PB1−PC
FB1=PB1−PF
PC−PBPB1−PC=PFPB1−PF
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)=−f−v−(−f)
−R+u−v+R=−f−v+f
u−RR−v=fv−f
uv−uf−Rv+Rf=Rf−vf
uv−uf−Rv=Rf−Rf−vf
uv−uf−Rv=−vf
uv−uf−2fv=−vf (R = 2f)
uv−uf=2fv−fv
uv−uf=fv
Dividing throughout by uvf, we will get :
1f−1v=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