The 200-in reflecting telescope at Mt.Palomar has an objective mirror with a focal length of 16.8 m.The effective aperture is the diameter of the 200-in mirror (200 in = 5.08 m).For light in the blue region (450 nm),what is the smallest angle between two stars that this telescope can ideally resolve? (In practice,the limit of resolution is due to atmospheric turbulence.) A)1.1 $\times$ 10^-8 rad B)1.1 $\times$ 10^-7 rad C)7.3 $\times$ 10^-7 rad D)1.1 $\times$ 10^-4 rad E)8.9 $\times$ 10^-5 rad

Question

Quizplus · Accepted Answer

The smallest angle that can be resolved by a telescope is given by the Rayleigh criterion:

θ = 1.22 λ/D

where θ is the smallest angle that can be resolved, λ is the wavelength of light, and D is the diameter of the objective mirror (i.e. the effective aperture).

Substituting the values given in the problem statement, we get:

θ = 1.22 (450 nm)/(5.08 m) = 1.1 x 10^-7 radians

Therefore, the answer is B, which is the closest to this value in scientific notation.

The 200-In Reflecting Telescope at Mt ×\times× 10-8 Rad B)1 ×\times× 10-7 Rad C)7

The 200-In Reflecting Telescope at Mt $\times$ 10^-8 Rad
B)1 $\times$ 10^-7 Rad
C)7