Angular Magnification in Telescope

Q. The magnifying power of an astronomical telescope in normal adjustment is $100.$ The distance between the objective and the eyepiece is $101\text{cm}$. The difference between the focal lengths of lenses will be $\left(\text{in cm}\right)$

Q. The magnifying power of an astronomical telescope is 8 and the distance between the two lenses is 54 cm. The focal length of eye lens and objective lens will be respectively

1. 6 cm and 48 cm
2. 48 cm and 6 cm
3. 8 cm and 64 cm
4. 64 cm and 8 cm

Q. A telescope has an objective lens of focal length $200\text{cm}$ and eye piece with focal length $2\text{cm}$. If this telescope is used to see a $50\text{m}$ tall building at a distance of $2\text{km}.$ What is the height of the image of the building formed by the objective lens is

1. $5\text{cm}$
2. $10\text{cm}$
3. $1\text{cm}$
4. $2\text{cm}$

Q. The focal lengths of the objective and eye-piece of a telescope are respectively $100cm$ and $2cm$. The moon subtends an angle of ${0.5}^{\circ }$ at the eye. If it is looked through the telescope, the angle subtended by the moon’s image will be

1. ${100}^{\circ }$
2. ${50}^{\circ }$
3. ${25}^{\circ }$
4. ${10}^{\circ }$

Q. The aperture diameter of a telescope is $5\text{m}$. The separation between the moon and the earth is $4\times {10}^5\text{km}$. With light of wavelength of $5500\mathring{\text{A}}$, the minimum separation between objects on the surface of the moon, so that they are just resolved, is close to:

1. $60\text{m}$
2. $20\text{m}$
3. $200\text{m}$
4. $600\text{m}$

Q.

A thin convex lens is made of two materials with refractive indices $n_1$ and $n_2$, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. $f$ is the focal length of the lens when $n_1=n_2=n$. The focal length is $f+\Delta f$ when $n_1=n$ and $n_2=n+\Delta n$. Assuming $\Delta n<<(n-1)$ and $(1<n<2)$, the correct statement(s) is/are:

1. $\left|\frac{\Delta f}{f}\right|<\left|\frac{\Delta n}{n}\right|$
2. The relation between $\frac{\Delta f}{f}$ and $\frac{\Delta n}{n}$ remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature.
3. If $\frac{\Delta n}{n}<0$ then $\frac{\Delta f}{f}>0$
4. For $n=1.5,\Delta n={10}^{-3}$ and $f=20cm,$ the value of $|\Delta f|$ will be $0.02cm$ (round off to $2^{nd}$ decimal place).

Q. (a) Draw a labelled ray diagram to obtain the real image formed by an astronomical telescope in normal adjustment position. Define its magnifying power.

(b) You are given three lenses of power 0.5 D, 4 D and 10 D to design a telescope.

(i) Which lenses should be used as objective and eyepiece ? Justify your answer.

(ii) Why is the aperture of the objective preferred to be large ?

Q. The diameter of the moon is $3.5\times {10}^{3}km$ and its distance from the earth is $3.8\times {10}^{5}km$. If it is seen through a telescope whose focal length for objective and eye lens are 4 m and 10 cm respectively, then the angle subtended by the image of the moon on the eye will be approximately

1. ${30}^{\circ }$
2. ${20}^{\circ }$
3. ${35}^{\circ }$
4. ${15}^{\circ }$

Q.

The walls of the halls built for music concerts should

1. Absorb sound

2. Amplify sound

3. Transmit sound

4. Reflect sound

Q. On what factors does the resolving power of a telescope depend?

Q. What will be the expression for the angular magnification produced by the telescope?

1. $m_{\theta }=\frac{f_e}{f_o}$
2. $m_{\theta }=\frac{f_o}{f_e}$
3. $m_{\theta }=\frac{1+f_e}{f_o}$
4. $m_{\theta }=\frac{1+f_o}{f_e}$

Q. The distance between the objective lens and the eye lens of an astronomical telescope when adjusted for parallel light is $100\text{cm}.$ The measured value of the magnification is $19.$ The focal length of the objective lens and the eye lens are-

1. $85\text{cm}$ and $5\text{cm}$
2. $190\text{cm}$ and $10\text{cm}$
3. $95\text{cm}$ and $5\text{cm}$
4. $50\text{cm}$ and $50\text{cm}$

Q. when an astronomical telescope is in normal adjustment, the magnification produced by it is M.If this is now turned around with the eyepiece facing a dis†an t object and the eye placed close to the objective , the magnification produced will

Q. (a) Draw a ray diagram depicting the formation of the image by an astronomical telescope in normal adjustment.
(b) You are given the following three lenses. Which two lenses will you use as an eyepiece and as an objective to construct an astronomical telescope ? Give reason.

Q. 21. an astronomical telescope of tenfold angular magnification has a length of 44 cm.the focal length of the objective is 1- 44cm 2- 440cm 3- 4cm 4- 40cm

Q. A Galileo telescope has an objective of focal length 100 cm and magnifying power 50. Tdistance between the two lenses in normal adjustment will be(1) 106 cm(3) 92 cm(2) 102 cm(4) 98 cm

Q.

Find the maximum magnifying power of a compound microscope having a 25 diopter lens as the objective, a 5 diopter lens as the eyepiece and the separation 30 cm between the two lenses. The least distance for clear vision is 25 cm.

Q. A thin non-conducting disc of radius R is uniformly charged with surface charge density $\sigma$. If potential at any point on the circumference of disc be $V$ and total electrostatic potential energy of the disc be $U$, then

1. $V=\frac{2\sigma R}{\pi {\epsilon }_0}$
2. $U=\frac{4}{3}\frac{{\sigma }^2{R}^3}{{\epsilon }_0}$
3. $V=\frac{\sigma R}{\pi {\epsilon }_0}$
4. $U=\frac{2{\sigma }^2{R}^3}{3{\epsilon }_0}$

Q. Focal length of the objective of a terrestrial telescope is $80\text{cm}$ and it is adjusted for parallel rays, then its magnifying power is $20$. If the focal length of erecting lens is $20\text{cm},$ then full length of telescope will be ( in $\text{cm}$)

1. $164$
2. $124$
3. $100$
4. $84$

Q. Magnifying power of a terrestrial telescope is $50$. Find the length of the telescope if focal length of eyepiece and erecting lens is $4\text{cm}$ and $6\text{cm}$ respectively.

1. $200\text{cm}$
2. $224\text{cm}$
3. $226\text{cm}$
4. $228\text{cm}$

Q. A small telescope has an objective lens of focal length 144cm andan eyepiece of focal length 6.0cm. What is the magnifying power ofthe telescope? What is the separation between the objective and the eyepiece?

Q. Diameter of the moon is $3.5\times {10}^{3}km$ and its distance from the earth is $3.8\times {10}^{5}km$. It is seen by a telescope whose objective and eyepiece have focal lengths $4m$ and $10cm$ respectively. The angular diameter of the image of the moon is (assume final image is at infinity)

1. $0.36radian$
2. $0.009radian$
3. $0.022radian$
4. $0.011radian$

Q. An astronomical telescope is to be designed to have a magnifying power of $50$ in normal adjustment. If the length of the tube is $102cm$, find the powers of the objective and the eyepiece.

1. $1;50$
2. $10;500$
3. $2;100$
4. $10;100$

Q. When diameter of the aperture of the objective of an astronomical telescope is increased, its

1. Magnifying power is increased and resolving power is decreased
2. Magnifying power and resolving power both are increased
3. Magnifying power remains the same but resolving power is increased
4. Magnifying power and resolving power both are decreased

Q.

Draw a ray diagram of an astronomical telescope for distant objects in normal adjustment. What is the expression for its magnifying power?

Q. The eyepiece of a refracting telescope has $f=9\text{cm}$. In the normal setting, seperation between objective and eyepiece is $1.8\text{m}$. Find the magnification.

1. $20$
2. $18$
3. $19$
4. $21$

Q. The focal length of the objective and eye piece of a telescope are respectively 60 cm and 10 cm. The magnitude of the magnifying power when the image is formed at infinity is

1. 50
2. 6
3. 70
4. 5

Q. The objective lens of an astronomical telescope has a focal length of $100\text{cm}$. The telescope is focused for normal vision of distant objects when tube length is $1.1\text{m}$. Find the magnifying power of the telescope.

1. $10$
2. $11$
3. $13$
4. $12$

Q. Focal length of the objective lens and the eyepiece of an astronomical telescope are $100\text{cm}$ and $2\text{cm}$ respectively. Find the angular magnification produced in the case of the least strain on the eye.

1. $70$
2. $50$
3. $60$
4. $80$

Q. The focal lengths of the lens of an astronomical telescope are $50\text{cm}$ and $5\text{cm}$. The length of the telescope when the image is formed at the least distance of distance vision is ( in $\text{cm}$ )

1. $\frac{250}{6}$
2. $\frac{275}{6}$
3. $\frac{325}{6}$
4. $\frac{350}{6}$