A telescope of aperture 3 × 10-2 m diameter is focused on a window at 80 m distance fitted with a wire mesh of spacing 3 × 10-3 m. Given: λ = 5.5 × 10-7 m, which of the following is true for observing the mesh through the telescope?

Question

A telescope of aperture 3 × 10-2 m diameter is focused on a window at 80 m distance fitted with a wire mesh of spacing 3 × 10-3 m. Given: λ = 5.5 × 10-7 m, which of the following is true for observing the mesh through the telescope? (A) Yes, it is possible with the same aperture size. (B) Possible also with an aperture half the present diameter. (C) No, it is not possible. (D) Given data is not sufficient.

Tardigrade Admin · Accepted Answer

Given: d= 3 × 10-2 m λ = 5.5 × 10-7 m Limit of resolution, Δθ = (1.22λ/d) = (1.22× 5.5× 10-7/3× 10-2) = 2.23 × 10-5 rad. At a distance of 80 m , the telescope is able to resolve between two points which are separated by 2.23 × 10-5×80 m = 1.78 × 10-3 m

Q. A telescope of aperture 3×10−2 m diameter is focused on a window at 80m distance fitted with a wire mesh of spacing 3×10−3 m. Given: λ= 5.5×10−7 m, which of the following is true for observing the mesh through the telescope?

Yes, it is possible with the same aperture size.

Possible also with an aperture half the present diameter.

No, it is not possible.

Given data is not sufficient.

Given : d=3×10−2m λ=5.5×10−7m Limit of resolution, Δθ=d1.22λ​ =3×10−21.22×5.5×10−7​=2.23×10−5rad. At a distance of 80 m , the telescope is able to resolve between two points which are separated by 2.23×10−5×80m =1.78×10−3m

Q. A telescope of aperture $3 \times 1 0^{- 2}$ m diameter is focused on a window at $80 m$ distance fitted with a wire mesh of spacing $3 \times 1 0^{- 3}$ m. Given: $λ =$ $5.5 \times 1 0^{- 7}$ m, which of the following is true for observing the mesh through the telescope?