(a) Draw the ray diagram of an astronomical telescope when the final image is formed at infinity. Write the expression for the resolving power of the telescope.
(b) An astronomical telescope has an objective lens of focal length 20 m and eyepiece of focal length 1 cm.
(i) Find the angular magnification of the telescope.
(ii) If this telescope is used to view the Moon, find the diameter of the image formed by the objective lens. Given the diameter of the Moon is 3·5 x 10⁶ m and radius of lunar orbit is 3·8 x 10⁸ m.

OR
(a) An object is placed in front of a concave mirror. It is observed that a virtual image is formed. Draw the ray diagram to show the image formation and hence derive the mirror equation 1/f = 1/u + 1/v
(b) An object is placed 30 cm in front of a plano-convex lens with its spherical surface of radius of curvature 20 cm. If the refractive index of the material of the lens is 1·5, find the position and nature of the image formed.

Question

(a) Draw the ray diagram of an astronomical telescope when the final image is formed at infinity. Write the expression for the resolving power of the telescope.
(b) An astronomical telescope has an objective lens of focal length 20 m and eyepiece of focal length 1 cm.
(i) Find the angular magnification of the telescope.
(ii) If this telescope is used to view the Moon, find the diameter of the image formed by the objective lens. Given the diameter of the Moon is 3·5 x 10⁶ m and radius of lunar orbit is 3·8 x 10⁸ m.

OR
(a) An object is placed in front of a concave mirror. It is observed that a virtual image is formed. Draw the ray diagram to show the image formation and hence derive the mirror equation 1/f = 1/u + 1/v
(b) An object is placed 30 cm in front of a plano-convex lens with its spherical surface of radius of curvature 20 cm. If the refractive index of the material of the lens is 1·5, find the position and nature of the image formed.

Infinity Learn · Accepted Answer

Resolving power of telescope = 𝐷 / 1.22𝜆b) (i) Angular magnification m=β/α=fo/fe=20m/10−2m=2000(ii) D/d=x/fod=Df0/x=3.5×106×20/3.8×108=.18mORA′B′AB=PB′PB−−−−−−1Also △A′B′F~MNP( for small curvature)∴A′B′MP=B′FPFA′B′AB=B′FPF−−−−−−−−−−−2From 1 and 2 PB′PB=B′FPF−−−−−−−−−3PB′PB=B′P+PFPF−−−−−−−−4PB=−u PB′=v PF=−fv−u=v−f−f−vf=−vu+uf1f=1v+1u(b) According to lens maker’s formula1/f=(μ−1)(1/R1−1/R2)for plano convex lens R1→R and R2→∞1/f=(μ−1)/R=(1.5−1)/20∴f=40cm(1/f)=(1/v)−(1/u)(1/40)=(1/v)−(1/−30)v=−12cmNature: virtual

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