Answer
Verified
409.8k+ views
Hint: To provide angular magnification of distant objects, the telescope is used. As the object is very far away, the objective has a large focal length and a much larger aperture than the eyepiece. To solve this question, we must know the formula for magnification in telescopes.
Formula Used: We will use the following formula to solve this question
$m = \dfrac{{{\alpha _i}}}{{{\alpha _o}}} = \dfrac{{{f_o}}}{{{f_e}}}$
Where
$m$ is the magnification
${\alpha _o}$ is the angle subtended by the object
${\alpha _i}$ is the angle subtended by the image
${f_o}$ is the focal length of objective
${f_e}$ is the focal length of the eyepiece
Complete Step-by-Step Solution:
Light enters the objective from a distant object and at its second focal point, a real and inverted image is formed.
This image acts as an eyepiece object; it magnifies this image and generates a final inverted image.
The following information is provided to us in the question
The focal length of objective, ${f_o} = 60 cm$
The focal length of the eyepiece, ${f_e} = 5 cm$
The angle subtended by the object, ${\alpha _o} = {2^ \circ }$
Now, let us use the formula given above
$m = \dfrac{{{\alpha _i}}}{{{\alpha _o}}} = \dfrac{{{f_o}}}{{{f_e}}}$
Let us now substitute the known values in the formula to get the required result
\[\dfrac{{{\alpha _i}}}{2} = \dfrac{{60}}{5}\]
Upon solving further, we get
\[\therefore {\alpha _i} = {24^ \circ }\]
Hence, the correct option is (B.)
Note: Real and highly diminished images are formed by a telescope. When an object is placed far from the focal length of a convergent lens, depending on how close the object is to the focal point, the lens produces an inverted, real and enlarged image. Telescopes are visual instruments used in the field of astronomy that use lenses and mirrors. There are many other classifications of telescopes according to their varying tasks.
Formula Used: We will use the following formula to solve this question
$m = \dfrac{{{\alpha _i}}}{{{\alpha _o}}} = \dfrac{{{f_o}}}{{{f_e}}}$
Where
$m$ is the magnification
${\alpha _o}$ is the angle subtended by the object
${\alpha _i}$ is the angle subtended by the image
${f_o}$ is the focal length of objective
${f_e}$ is the focal length of the eyepiece
Complete Step-by-Step Solution:
Light enters the objective from a distant object and at its second focal point, a real and inverted image is formed.
This image acts as an eyepiece object; it magnifies this image and generates a final inverted image.
The following information is provided to us in the question
The focal length of objective, ${f_o} = 60 cm$
The focal length of the eyepiece, ${f_e} = 5 cm$
The angle subtended by the object, ${\alpha _o} = {2^ \circ }$
Now, let us use the formula given above
$m = \dfrac{{{\alpha _i}}}{{{\alpha _o}}} = \dfrac{{{f_o}}}{{{f_e}}}$
Let us now substitute the known values in the formula to get the required result
\[\dfrac{{{\alpha _i}}}{2} = \dfrac{{60}}{5}\]
Upon solving further, we get
\[\therefore {\alpha _i} = {24^ \circ }\]
Hence, the correct option is (B.)
Note: Real and highly diminished images are formed by a telescope. When an object is placed far from the focal length of a convergent lens, depending on how close the object is to the focal point, the lens produces an inverted, real and enlarged image. Telescopes are visual instruments used in the field of astronomy that use lenses and mirrors. There are many other classifications of telescopes according to their varying tasks.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE