Question
A 5.0 diopter lens forms a virtual image which is 4 times the object placed perpendicularly on the principal axis of the lens. Find the distance of the object from the lens.
✓
Answer
Given, P = 5 diopter (convex lens)$\Rightarrow\text{f}=\frac{1}{5}\text{m}=20\text{cm}$Since, a virtual image is formed, u and v both are negative.Given, $\frac{\text{v}}{\text{u}}=4$$\Rightarrow\text{v}=4\text{u} \ ...(1)$
From lens formula, $\frac{1}{\text{v}}-\frac{1}{\text{u}}=\frac{1}{\text{f}}$$\Rightarrow\frac{1}{\text{f}}=\frac{1}{4\text{u}}-\frac{1}{\text{u}}\Rightarrow\frac{1}{20}=\frac{1-4}{4\text{u}}=-\frac{3}{4\text{u}}$
$\Rightarrow\text{u}=-15\text{cm}$
$\therefore$ Object is placed 15cm away from the lens.
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
Distinguish between nuclear fission and fusion. Show how in both these processes energy is released. Calculate the energy release in MeV in the deuterium-tritium fusion reaction:
$^{2}_{1}\text{H} + ^{3}_{1}\text{H}\rightarrow^{4}_{2}\text{H} +\text{n}$
Using the data:
$\text{m}(^{2}_{1}\text{H}) = 2.014102 \text{u}$
$\text{m}(^{3}_{1}\text{H}) = 3.016049\text{u}$
$\text{m}(^{4}_{2}\text{H}) = 4.002603 \text{u}$
$\text{m}_{n} = 1.008665 \text{n}$
$1\text{u} = 931.5\text{MeV/c}^{2}$.
→$^{2}_{1}\text{H} + ^{3}_{1}\text{H}\rightarrow^{4}_{2}\text{H} +\text{n}$
Using the data:
$\text{m}(^{2}_{1}\text{H}) = 2.014102 \text{u}$
$\text{m}(^{3}_{1}\text{H}) = 3.016049\text{u}$
$\text{m}(^{4}_{2}\text{H}) = 4.002603 \text{u}$
$\text{m}_{n} = 1.008665 \text{n}$
$1\text{u} = 931.5\text{MeV/c}^{2}$.
Two charges $3 \times 10^{-8} C$ and $-2 \times 10^{-8} C$ are located $15 cm$ apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
→- Derive the relation between the decay constant and half life of a radioactive substance.
- A radioactive element reduces to 25% of its initial mass in 1000 years. Find its half life.
A small telescope has an objective lens of focal length 144 cm and an eyepiece of focal length 6.0 cm. What is the magnifying power of the telescope? What is the separation between the objective and the eyepiece?
Define the term “cut off frequency” in photoelectric emission. The threshold frequency of a metal is f. When the light of frequency 2f is incident on the metal plate, the maximum velocity of photo-electrons is $v_1$. When the frequency of the incident radiation is increased to 5f, the maximum velocity of photo-electrons is $v_2$. Find the ratio $v_1 : v_2.$
→What is the area of the plates of a 2F parallel plate capacitor, given that the separation between the plates is 0.5 cm? [You will realise from your answer why ordinary capacitors are in the range of μF or less. However, electrolytic capacitors do have a much larger capacitance (0.1F) because of very minute separation between the conductors.]
You are given a circuit below. Write its truth table. Hence, identify the logic operation carried out by this circuit. Draw the logic symbol of the gate it corresponds to.
A point charge is moving along a straight line with a constant velocity u. Consider a small area A perpendicular to the direction of motion of the charge (El). Calculate the displacement current through the area when its distance from the charge is x. The value of x is not large so that the electric field at any instant is essentially given by Coulomb's law.
Drive the formula of electric field for points on the equatorial plane at distance $r$ from the centre of electric dipole.
→In a typical fission reaction, the nucleus is split into two middle-weight nuclei of unequal masses. Which of the two (heavier or lighter) has greater kinetic energy? Greater linear momentum?