Answer
Verified
433.8k+ views
Hint: In a Galilean telescope, the focal length of the objective lens is equal to the difference between the length between the two lenses and the focal length of the eye-piece, ${f_o} = L + {f_e}$, where ${f_o},{f_e}$ are the focal lengths of objective lens and eye-piece, L is the distance between them. Substitute the values of L and focal length of the objective lens to find the value of focal length of the eye-piece. Magnification is the negative ratio of focal length of the objective lens and focal length of the eye-piece.
Complete step by step answer:
We are given that a Galilean telescope measures 9 cm from the objective to the eye-piece and the focal length of the objective is 15 cm.
We have to find its magnifying power.
As we can see in the above figure, the objective is a convex lens and the eye-piece is a concave lens.
So the focal length is negative for the concave (eye-piece) lens.
As we can see, the focal length of the objective lens is the sum of the focal length of the eye-piece and the distance between them.
${f_o} = L + {f_e}$, where ${f_o},{f_e}$ are the focal lengths of objective lens and eye-piece, L is the distance between them and ${f_e}$ should be taken negatively.
$
{f_o} = L + \left( { - {f_e}} \right) \\
\implies {f_o} = L - {f_e} \\
\implies {f_e} = L - {f_o} \\
$
Substitute the values of the L and ${f_o}$ as they are given in the question.
$
{f_o} = 15cm,L = 9cm \\
\implies {f_e} = L - {f_o} \\
= 9 - 15 \\
\therefore {f_e} = - 6cm \\
$
Magnification is the negative ratio of focal length of the objective lens and focal length of the eye-piece.
$
m = \dfrac{{ - {f_o}}}{{{f_e}}} \\
{f_o} = 15cm,{f_e} = - 6cm \\
m = \dfrac{{ - 15}}{{ - 6}} \\
\implies m = \dfrac{5}{2} \\
\therefore m = + 2.5 \\
$
The magnifying power of the given Galilean telescope is 2.5.
So, the correct answer is “Option A”.
Note:
The objective lens is concave, which is a spherical lens and focuses the light rays passed through it to a specific point. Eye-piece is a convex lens, which is a spherical lens and diverges the light rays refracted from it. The lenses used in objective and eye-piece are not the same in a Galilean telescope. Be careful in considering the lenses.
Complete step by step answer:
We have to find its magnifying power.
As we can see in the above figure, the objective is a convex lens and the eye-piece is a concave lens.
So the focal length is negative for the concave (eye-piece) lens.
As we can see, the focal length of the objective lens is the sum of the focal length of the eye-piece and the distance between them.
${f_o} = L + {f_e}$, where ${f_o},{f_e}$ are the focal lengths of objective lens and eye-piece, L is the distance between them and ${f_e}$ should be taken negatively.
$
{f_o} = L + \left( { - {f_e}} \right) \\
\implies {f_o} = L - {f_e} \\
\implies {f_e} = L - {f_o} \\
$
Substitute the values of the L and ${f_o}$ as they are given in the question.
$
{f_o} = 15cm,L = 9cm \\
\implies {f_e} = L - {f_o} \\
= 9 - 15 \\
\therefore {f_e} = - 6cm \\
$
Magnification is the negative ratio of focal length of the objective lens and focal length of the eye-piece.
$
m = \dfrac{{ - {f_o}}}{{{f_e}}} \\
{f_o} = 15cm,{f_e} = - 6cm \\
m = \dfrac{{ - 15}}{{ - 6}} \\
\implies m = \dfrac{5}{2} \\
\therefore m = + 2.5 \\
$
The magnifying power of the given Galilean telescope is 2.5.
So, the correct answer is “Option A”.
Note:
The objective lens is concave, which is a spherical lens and focuses the light rays passed through it to a specific point. Eye-piece is a convex lens, which is a spherical lens and diverges the light rays refracted from it. The lenses used in objective and eye-piece are not the same in a Galilean telescope. Be careful in considering the lenses.
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
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
10 examples of evaporation in daily life with explanations
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Why is there a time difference of about 5 hours between class 10 social science CBSE