SATHEE: Optics 5 Question 1

Optics 5 Question 1

1. The value of numerical aperture of the objective lens of a microscope is 1.25 . If light of wavelength $5000 \AA$ is used, the minimum separation between two points, to be seen as distinct, will be

(2019 Main, 12 April I)

(a) $0.24 μ m$

(b) $0.38 μ m$

(d) $0.48 μ m$

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Answer:

Correct Answer: 1. (a)

Solution:

Key Idea Numerical Aperture (NA) of the microscope is given by $N A = \frac{0.61 λ}{d}$

Here, $d =$ minimum separation between two points to be seen as distinct and $λ$ =wavelength of light.

Given, $λ = 5000 \AA = 5000 \times 10^{- 10} m$ and

$N A = 1.25$

Now, $d = \frac{0.61 λ}{N A} = \frac{0.61 \times 5000 \times 10^{- 10}}{1.25}$

$\begin{aligned} d & = \frac{3.05}{1.25} \times 10^{- 7} m \\ = 2.4 \times 10^{- 7} m \\ d & = 0.24 μ m \end{aligned}$

2 Limit of resolution for a telescope from Rayleigh’s criteria is

$θ_{R} = \frac{1.22 λ}{D}$

Here, $D = 250 c m = 250 \times 10^{- 2} m$

and $λ = 600 n m = 600 \times 10^{- 9} m$

So, limit of resolution is

$\begin{aligned} θ_{R} & = \frac{1.22 \times 600 \times 10^{- 9}}{250 \times 10^{- 2}} \\ = 2.93 \times 10^{- 7} r a d \\ \approx 3 \times 10^{- 7} r a d \end{aligned}$

3 For a telescope, limit of resolution is

$given by Δ θ = \frac{1.22 λ}{D}$

Here, $λ = 500 n m = 500 \times 10^{- 9} m$ ,

$D = 200 c m = 200 \times 10^{- 2} m$

So, limit of resolution is $Δ θ = \frac{1.22 \times 500 \times 10^{- 9}}{200 \times 10^{- 2}}$

$= 305 \times 10^{- 9} r a d$

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Optics 5 Question 1

1. The value of numerical aperture of the objective lens of a microscope is 1.25 . If light of wavelength $5000 \AA$ is used, the minimum separation between two points, to be seen as distinct, will be

Answer:

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सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Optics 5 Question 1

1. The value of numerical aperture of the objective lens of a microscope is 1.25 . If light of wavelength 5000\AA is used, the minimum separation between two points, to be seen as distinct, will be

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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1. The value of numerical aperture of the objective lens of a microscope is 1.25 . If light of wavelength $5000 \AA$ is used, the minimum separation between two points, to be seen as distinct, will be