Collecting Power of Telescopes | AQA A Level Physics Revision Notes 2017

Collecting Power

Telescopes are designed to gather as much light as possible
- The more light energy a telescope can gather, the brighter the images it will be able to produce
- This can be measured by a telescope's collecting power

The collecting power of a telescope is defined as:

A measure of the amount of light energy it collects per second

This is equivalent to the power per unit area, or intensity of the incident radiation collected

Differences in Collecting Power

9-1-6-collecting-power

The telescope with the larger aperture is able to produce a brighter image

The collecting power of a telescope is directly proportional to the square of the diameter of its objective

$c o l l e c t i n g p o w e r \propto D^{2}$

This is because:
- Intensity is proportional to surface area
- The surface area of a circular object of diameter D is equal to $\frac{π D^{2}}{4}$

This means that objects at greater distances can also be seen
- The intensity of light from a point source decreases inversely with the square of the distance from the inverse square law

Large Diameter Telescopes

Larger aperture diameter telescopes are advantageous for two main reasons:
- They have a greater collecting power so images are brighter
- They have a greater resolving power so images are clearer

The collecting power of two telescopes can be calculated using the ratio

$\frac{c o l l e c t i n g p o w e r o f t e l e s c o p e 1}{c o l l e c t i n g p o w e r o f t e l e s c o p e 2} = {(\frac{D_{1}}{D_{2}})}^{2}$

The resolving power of two telescopes operating at the same wavelength can be calculated using the ratio

$\frac{r e s o l v i n g p o w e r o f t e l e s c o p e 1}{r e s o l v i n g p o w e r o f t e l e s c o p e 2} = \frac{θ_{1}}{θ_{2}} = \frac{\frac{λ}{D_{1}}}{\frac{λ}{D_{2}}} = \frac{D_{2}}{D_{1}}$

Worked example

The largest refracting telescope still in operation is the Yerkes refractor. The construction of this telescope later paved the way for the Otto Struve reflector to be built. Both telescopes detect optical wavelengths of light.

The table below summarises some of the properties of the two optical telescopes.

Telescope	Type	Objective diameter / cm
Yerkes	refractor	102
Otto-Struve	reflector	208

Compare the two telescopes in terms of their collecting power and resolving power.

Answer:

Step 1: Compare the collecting power of the telescopes

Since collecting power, or intensity of light collected $\propto$ area $\propto$ (diameter)²

$\frac{c o l l e c t i n g p o w e r o f r e f l e c t o r}{c o l l e c t i n g p o w e r o f r e f r a c t o r} = {(\frac{D_{r e f l e c t o r}}{D_{r e f r a c t o r}})}^{2}$

$\frac{c o l l e c t i n g p o w e r o f r e f l e c t o r}{c o l l e c t i n g p o w e r o f r e f r a c t o r} = {(\frac{208}{102})}^{2} = 4.16 \approx 4$

The collecting power of the Otto-Struve reflector is 4 times greater than the Yerkes refractor, meaning it will produce brighter images

Step 2: Compare the resolving power of the telescopes

Resolving power, or minimum angular resolution: $θ \propto \frac{1}{D}$ (for the same wavelength)

$\frac{θ_{r e f l e c t o r}}{θ_{r e f r a c t o r}} = \frac{D_{r e f r a c t o r}}{D_{r e f l e c t o r}}$

$\frac{θ_{r e f l e c t o r}}{θ_{r e f r a c t o r}} = \frac{102}{208} = 0.49 \approx 0.5$

The Yerkes refractor can resolve detail half as well as the Otto-Struve reflector
Therefore, the resolving power of the Otto-Struve reflector is twice as great as the Yerkes refractor, meaning it will produce clearer images

Examiner Tip

Remember: the smaller the value of θ, the greater the resolving power

Collecting Power of Telescopes (AQA A Level Physics)

Revision Note