Chapter 35: Q. 25 (page 1017)

Two light bulbs are $1.0 m$ apart. from, what distance can these light bulbs be marginally resolved by a small telescope with a $4.0 - c m - d i a m e t e r$ objective lens? assume that the lens is diffraction limited and $λ = 600 n m$ .

Short Answer

Expert verified

Light bulbs be marginally resolved by a small telescope with a $4.0 - c m - d i a m e t e r$ objective lens with distance $L = 55.5 K m$ .

Step by step solution

Given information

We have given that:
Distance between two bulbs is $d = 1.0 c m$ ,

the diameter islocalid="1648894941098" $D = 4.0 c m$ ,

the wavelength islocalid="1648894948467" $λ = 600 n m \to 600 \times 10^{- 9} m$ .

We need to find the distance.

Simplification

Releigh's criteria for angular resolution for circular diameter, $D > > h, i s$ :

$d θ = \frac{1.22 λ}{D}$

$d θ = \frac{1.22 \times 600 \times 10^{- 9}}{0.04}$

$d θ = 18 \times 10^{- 6}$

Now we have to find L from,
$d θ = \frac{d}{L}$

By multiplying both the sides by L,

localid="1648895025315" $L \times d θ = L$ localid="1648895031802" $\times \frac{d}{L}$

localid="1648895036807" $L \times d θ = d$ .

Dividing both the sides by $d θ$ ,

localid="1648895043506" $\frac{L \times d θ}{d θ} = \frac{d}{d θ}$

$L = \frac{d}{d θ}$ .

Substitute the values in equation,

$L = \frac{1.0}{18 x 10^{- 6}}$

$L = 55.5 k m .$

Here, $L$ is the distance that these light bulbs can be marginally resolved by a small telescope.

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Two light bulbs are $1.0 m$ apart. from, what distance can these light bulbs be marginally resolved by a small telescope with a $4.0 - c m - d i a m e t e r$ objective lens? assume that the lens is diffraction limited and $λ = 600 n m$ .

Short Answer

Step by step solution

Given information

Simplification

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Two light bulbs are 1.0mapart. from, what distance can these light bulbs be marginally resolved by a small telescope with a 4.0-cm-diameterobjective lens? assume that the lens is diffraction limited andλ=600nm.

Short Answer

Step by step solution

Given information

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Electricity and Magnetism

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Study anywhere. Anytime. Across all devices.

Two light bulbs are $1.0 m$ apart. from, what distance can these light bulbs be marginally resolved by a small telescope with a $4.0 - c m - d i a m e t e r$ objective lens? assume that the lens is diffraction limited and $λ = 600 n m$ .