Question

The resolving limit of a telescope with objective diameter of 1 inch and light of wave length 6000 A° is - 
1. 2.88 × 10^-5 radian
2. 3.9 × 10^-4 radian
3. 2.9 × 10^-7 radian
4. 3.9 × 10⁶ radian

Answer 1

Correct Answer - Option 1 : 2.88 × 10^-5 radian

Concept:

Resolving Power

• The reciprocal of the smallest angle subtended at the objective lens of a telescope by two point objects which can be just distinguished as separate is called resolving power of a telescope.

The resolving power of a telescope is given by:

\(Resolving\;power\;\left( {R.P} \right) = \frac{D}{{1.22\;λ }}\)

Where D is the distance between two-point objects and λ is wavelength of light used.

Calculation:

Given wavelength λ = 6000 A° = 6000 × 10 ^-10 m

length D = 1 inch = 2.54 cm = 0.254 m

\(Resolving\;power\;\left( {R.P} \right) = \frac{6000 \times 10^{10}m}{{1.22\times 0.254 }}\)

Resolving Power = 2.88 × 10-5 radian

So, the correct option is  2.88 × 10-5 radian.