Download App

Ray Optics and Optical Instruments — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsRay Optics and Optical Instruments5 Marks
Question
Define magnifying power of a telescope. Write its expression.
A small telescope has an objective lens of focal length 150 cm and an eye piece of focal length 5 cm. If this telescope is used to view a 100m high tower 3 km away, find the height of the final image when it is formed 25 cm away from the eye piece.
✓

Answer

  1. Magnifying power is the ratio of the angle subtended at the eye by the image to the angle subtended at the unaided eye by the object.
Expression
$\text{m} = \beta\big/\alpha = \text{f}_{o}\big/\text{f}_{e}$
or $\text{m} = \text{f}_{o} /_{ \text{f}_{e}}\bigg(1 + \frac{\text{f}_{e}}{\text{D}}\bigg)$
  1. Using, the lens equation for objective lens,:
$\frac{1}{\text{f}_{o}} =\frac{1}{\text{v}_{o}}-\frac{1}{\text{u}_{o}}$
$ => \frac{1}{150} = \frac{1}{\text{v}_{o}} - \frac{1}{-3\times10^{5}}$
$ => \frac{1}{\text{v}_{o}} =\frac{1}{150} -\frac{1}{-3\times10^{5}} = \frac{2000-1}{3\times10^{5}}$
$ =>\text{v}_{o} = \frac{3\times10^{5}}{1999}\text{cm}$
$\approx 150 \text{cm}$
Hence, magnification due to the objective lens
$\text{m}_{o} =\frac{\text{v}_{o}}{\text{u}_{o}} = \frac{150\times10^{-2}\text{m}}{3000\text{m}}$
$\approx\frac{10^{-2}}{20} = .05\times10^{-2}$
Using lens formula for eyepiece
$\frac{1}{\text{f}_{e}} =\frac{1}{\text{v}_{e}} - \frac{1}{\text{u}_{e}}$
$ = > \frac{1}{5} = \frac{1}{-25} -\frac{1}{\text{u}_{e}}$
$ = > \frac{1}{\text{u}_{e}} =\frac{1}{-25} - \frac{1}{5} = \frac{-1-5}{25}$
$ = >\text{u}_{e} =\frac{-25}{6}\text{cm}$
$\therefore\text{ Magnification due to eyepiece} \text{ m}_{e} =\frac{-25}{-\frac{25}{6}}= 6 $
Hence, total magnification $ = > \text{m} = \text{m}_{e}\times\text{m}_{o}$
$\text{m} = 6 \times5\times10^{-4} = 30 \times10^{-4}$
Hence, size of final image
$ = 30 \times10^{-4}\times100 \text{m}$
$ = 30 \text{ cm}.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Ray Optics and Optical Instruments→Ray Optics and Optical Instruments — all question types→Physics STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Explain the variation of conductivity with temperature for:
  1. A metallic conductor.
  2. Ionic conductors.
  3. Semiconductors.
→
A bucket full of water is placed in a room at $15^\circ C$ with initial relative humidity $40\%$. The volume of the room is $50m^3$.
  1. How much water will evaporate?
  2. lf the room temperature is increased by $5^\circ C,$ how much more water will evaporate? The saturation vapour pressure of water at $15^\circ C$ and $20^\circ C$ are $1.6\ kPa$ and $2.4\ kPa$ respectively.
→
The gravitational pontential in a region is given by V = (20N/kg) (x + y).
  1. Show that the equation is dimensionally correct.
  2. Find the gravitational field at the point (x, y). Leave your answer in terms of the unit vectors $\overrightarrow{\text{i}},\ \overrightarrow{\text{j}},\ \overrightarrow{\text{k}}.$
  3. Calculate the magnitude of the gravitational force on a particle of mass 500g placed at the origin.
→
If a proton had a radius $R$ and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a $H-$ atom when:
  1. $R = 0.1 \mathring A .$
  2. $R = 10 \mathring A .$
→
0.040g of He is kept in a closed container initially at 100.0°C. The container is now heated. Neglecting the expansion of the container, calculate the temperature at which the internal energy is increased by 12J.
→
Two charges $2.0 \times 10^{-6}C$ and $1.0 \times 10^{-6}C$ are placed at a separation of $10\ cm$. Where should a third charge be placed such that it experiences no net force due to these charges?
→
A magnetic field $B$ is confined to a region $ r \leq$ a and points out of the paper $($the $z-$ axis$), r = 0$ being the centre of the circular region. $A$ charged ring $ ($charge $= Q)$ of radius $b, b > a$ and mass m lies in the $x-y$ plane with its centre at the origin. The ring is free to rotate and is at rest. The magnetic field is brought to zero in time $\triangle t$. Find the angular velocity $\omega$ of the ring after the field vanishes.
→
Explain the uses of Polaroid.
→
A particle stays at rest as seen in a frame. We can conclude that:
  1. The frame is inertial.
  2. Resultant force on the particle is zero.
  3. The frame may be inertial but the resultant force on the particle is zero.
  4. The frame may be non-inertial but there is a non-zero resultant force.
→
a. State the condition for resonance to occur in series LCR a.c. circuit and derive an expression for resonant frequency.
b. Draw a plot showing the variation of the peak current $\left( i _{ m }\right)$ with frequency of the a.c, source used. Define the quality factor Q of the circuit.
→