Q.Assume that light of wavelength $0.5\,\mu m$ is coming from a star. What is the limit of angular resolution in radians of a telescope whose objective has a radius 122 cm.?

Resolving Power of a Telescope – From Intuition to Precision

Imagine you are looking at two stars that are very close together in the night sky. Through a small telescope, they might appear as a single blurry blob. Through a larger telescope, you see them as two distinct points. Why? The answer is not about magnification — it is about resolution, the ability to distinguish fine detail.

The Core Intuition

Light behaves like a wave. When it enters a telescope, it passes through the circular opening (the aperture) and diffracts — it spreads out slightly. Even a perfect lens cannot focus light to an infinitely sharp point. Instead, it produces a small central bright spot surrounded by faint rings, called an Airy pattern. This is not a flaw in the lens; it is a fundamental property of wave optics.

If two stars are extremely close, their Airy patterns overlap. When the overlap is too great, your eye cannot tell that there are two sources — they merge into one. The resolving power of a telescope is its ability to show two closely spaced objects as separate.

The Rayleigh Criterion

There is a precise condition for when two point sources are just barely resolvable. It is called the Rayleigh criterion:

Two sources are resolved when the central maximum of one falls on the first minimum of the other.

For a circular aperture, the angular separation $\Delta\theta$ (in radians) at which this happens is:

where:

• $\lambda$ is the wavelength of light
• $D$ is the diameter of the telescope's objective (the main lens or mirror)

Why 1.22?

The factor 1.22 comes from the mathematics of diffraction through a circular opening. It is the first zero of the Bessel function that describes the Airy pattern. For a slit (a rectangular opening), the factor would be 1.00 — but telescopes have circular apertures, so 1.22 is the number you need.

A Concrete Example

Suppose you use a telescope with $D = 10$ cm and observe yellow light with $\lambda = 550$ nm ($5.5 \times 10^{-7}$ m). Then:

That is about 1.4 arcseconds. Two stars closer than this would appear as one.

Now double the aperture to $D = 20$ cm. The resolving angle halves to $3.35 \times 10^{-6}$ radians (about 0.7 arcseconds). You can now separate stars that are twice as close.

What Resolving Power Is NOT …