Question
A compound microscope has a magnifying power of $100$ when the image is formed at infinity. The objective has a focal length of $0.5\ cm$ and the tube length is $6.5\ cm$. Find the focal length of the eyepiece.
✓
Answer
For the give compound microscope$, f_0 = 0.5\ cm,$ tube length $= 6.5\ cm$ magnifying power $= 100\ ($normal adjustment$)$
Since, the image is formed at infinity, the real image produced by the objective lens should lie on the focus of the eye piece.
So$, v_o + f_e = 6.5\ cm ...(1)$
Again, magnifying power $\text{m}=\frac{\text{v}_0}{\text{u}_0}\times\frac{\text{D}}{\text{f}_\text{e}}\ [$for normal adjustment$]$
$\Rightarrow\text{m}=\Big[1-\frac{\text{V}_0}{\text{f}_0}\Big]\frac{\text{D}}{\text{f}_\text{e}}$
$\Rightarrow100=-\Big[1-\frac{\text{V}_0}{0.5}\Big]\times\frac{25}{\text{f}_\text{e}}\ [$Taking $D = 25\ cm]$
$\Rightarrow100\text{f}_\text{e}=-(1-2\text{v}_0)\times25$
$\Rightarrow2\text{v}_0-4\text{f}_\text{e}=1 ...(2)$
Solving equation $(1)$ and $(2)$ we can get,
$V_0 = 4.5\ cm$ and $f_e = 2\ cm$
So, the focal length of the eye piece is $2\ cm.$
Since, the image is formed at infinity, the real image produced by the objective lens should lie on the focus of the eye piece.
So$, v_o + f_e = 6.5\ cm ...(1)$
Again, magnifying power $\text{m}=\frac{\text{v}_0}{\text{u}_0}\times\frac{\text{D}}{\text{f}_\text{e}}\ [$for normal adjustment$]$
$\Rightarrow\text{m}=\Big[1-\frac{\text{V}_0}{\text{f}_0}\Big]\frac{\text{D}}{\text{f}_\text{e}}$
$\Rightarrow100=-\Big[1-\frac{\text{V}_0}{0.5}\Big]\times\frac{25}{\text{f}_\text{e}}\ [$Taking $D = 25\ cm]$
$\Rightarrow100\text{f}_\text{e}=-(1-2\text{v}_0)\times25$
$\Rightarrow2\text{v}_0-4\text{f}_\text{e}=1 ...(2)$
Solving equation $(1)$ and $(2)$ we can get,
$V_0 = 4.5\ cm$ and $f_e = 2\ cm$
So, the focal length of the eye piece is $2\ cm.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A gas is enclosed in a cylindrical can fitted with a piston. The walls of the can and the piston are adiabatic. The initial pressure, volume and temperature of the gas are $100kPa, 400\ cm^3$ and $300K,$ respectively. The ratio of the specific heat capacities of the gas is $\frac{\text{C}_\text{P}}{\text{C}_\text{V}}=1.5.$ Find the pressure and the temperature of the gas if it is,
→- Suddenly compressed.
- Slowly compressed to $100\ cm^3.$
What is capacitance of a conductor? What is its unit? Find the formula for capacitance of an isolated spherical conductor. Draw a graph between capacitance and radius. If a spherical conductor is placed in dielectric constant $\epsilon_r$, then what will be the effect on the value of capacitance?###If the area of each conducting plate of a parallel plate capacitor is A and the separation between them is $d$, then express the formula for its capacitance.
→Explain the laws of refraction of light waves on the basis of Huygen's theory of secondary wavelets.
Two capacitors of capacitances $20.0\ pF$ and $50.0\ pF$ are connected in series with a $6.00V$ battery. Find:
$a.$ The potential difference across each capacitor.
$b.$ The energy stored in each capacitor.
→$a.$ The potential difference across each capacitor.
$b.$ The energy stored in each capacitor.
Three coplanar parallel wires, each carrying a current of 10A along the same direction, are placed with a separation 5.0cm between the consecutive ones. Find the matnitude ol the magnetic force per unit lenght acting on the wires.
A simple pendulum is constructed by hanging a heavy ball by a $5.0m$ long string. It undergoes small oscillations.
→- How many oscillations does it make per second?
- What will be the frequency if the system is taken on the moon where acceleration due to gravitation of the moon is $1.67\ m/s^2.$
A wire of resistance $15.0\Omega$ is bent to form a regular hexagon ABCDEFA. Find the equivalent resistance of the loop between the points (a) A and B (b) A and C and (c) A and D.
→Two long, straight wires, each carrying a current of $5A,$ are placed along the $X$ and $Y-$ axes respectively. The currents point along the positive directions of the axes. Find the magnetic fields at the points $(a) (1m, 1m), (b) (-1m, 1m), (c) (-1m,-1m)$ and $(d) (1m, -1m),$
→A particle of mass m and charge $q$ is thrown at a speed u against a uniform electric field $E$. How much distance will it travel before coming to momentary rest?
→A rectangular wire loop of sides 8 cm and 2 cm having a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is $1 cm s ^{-1}$ in a direction normal to the (a) longer side (b) shorter side of the loop? For how long does the induced voltage last in each case?
→