SATHEE: Optics 6 Question 8

Optics 6 Question 8

9. A planet is observed by an astronomical refracting telescope having an objective of focal length $16 m$ and an eyepiece of focal length $2 c m$

(1992, 2M)

(a) the distance between the objective and the eyepiece is $16.02 m$

(b) the angular magnification of the planet is -800

(d) the objective is larger than the eyepiece

Fill in the Blank

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Solution:

Key Idea In a YDSE, path difference between 2 rays, reaching at some common point $P$ located at angular position ’ $θ$ ’s shown in the figure below is

$Δ L = d \sin θ$

For small value of $θ; \sin θ \approx θ$

So, path difference $= Δ L = d θ$

For a bright fringe at same angular position ’ $θ$ ‘, both of the rays from slits $S_{1}$ and $S_{2}$ are in phase.

Hence, path difference is an integral multiple of wavelength of light used.

$\begin{aligned} i.e., & Δ L & = n λ \\ or & d θ & = n λ \Rightarrow λ = \frac{d θ}{n} \end{aligned}$

Here, $θ = \frac{1}{40} r a d, d = 0.1 m m$ Hence, $λ = \frac{0.1}{40 n} m m = \frac{0.1 \times 10^{- 3} m}{40 n}$

$\begin{aligned} = \frac{0.1 \times 10^{- 3} \times 10^{9}}{40 n} n - m \\ \Rightarrow λ & = \frac{2500}{n} n - m \end{aligned}$

So, with light of wavelength $λ_{1}$ we have

$λ_{1} = \frac{2500}{n_{1}} (n - m)$

and with light of wavelength $λ_{2}$ , we have

$λ_{2} = \frac{2500}{n_{2}} (n - m)$

Now, choosing different integral values for $n_{1}$ and $n_{2}$ , (i.e., $n_{1}, n_{2} = 1, 2, 3 \dots$ etc) we find that for

$n_{1} = 4, λ_{1} = \frac{2500}{4} = 625 n - m$

and for $n_{2} = 5$ ,

$λ_{2} = \frac{2500}{5} = 500 n - m$

These values lie in given interval $500 n - m$ to $625 n - m$ .

पिछला

अगला

Optics 6 Question 8

9. A planet is observed by an astronomical refracting telescope having an objective of focal length $16 m$ and an eyepiece of focal length $2 c m$

Fill in the Blank

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Optics 6 Question 8

9. A planet is observed by an astronomical refracting telescope having an objective of focal length 16m and an eyepiece of focal length 2cm

Fill in the Blank

Solution:

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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9. A planet is observed by an astronomical refracting telescope having an objective of focal length $16 m$ and an eyepiece of focal length $2 c m$