- JEE Mains 2017
- Hard
- MCQ
In an experiment a convex lens of focal length \(15\, cm\) is placed coaxially on an optical bench in front of a convex mirror at a distance of \(5\,cm\) from it. It is found that an object and its image coincide, if the object is placed at a distance of \(20\,cm\) from the lens. The focal length of the convex mirror is.......\(cm\)
Answer & Solution
(A) \(27.5\)
Step-by-step Solution
Detailed explanation
object is placed at a distance \((u)=-20\, \mathrm{cm}\)
By lens formula,
\(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\)
\(\frac{1}{v} = \frac{1}{f} + \frac{1}{u}\)
\( = \frac{1}{{15}} - \frac{1}{{20}}\)
\(\frac{1}{v}=\frac{4-3}{60}\)
\({v}=60\, \mathrm{cm}\)
The image \(I\) gets formed at \(60\,\mathrm{cm}\) to the right of the lens and it wil be inverted.
The rays from the image \((I)\) formed further falls on the convex mirror forms another image This image should formed in such a way that it coincide with object at the same point due to reflection takes place by convex mirror.
Distance between lens and mirror will be \(\mathrm{d}\,=\) imagedistance \((\mathrm{v})\,-\) radius of curvature of convex mirror.
\(5=60-2 f\)
\(2 f=60-5\)
\(\mathrm{f}=\frac{55}{2}=27.5\, \mathrm{cm}\) (convex mirror)
More questions from Physics
- A particle executes simple harmonic motion with an amplitude of \(4 \mathrm{~cm}\). At the mean position, velocity of the particle is \(10 \mathrm{~cm} / \mathrm{s}\). The distance of the particle from the mean position when its speed becomes \(5 \mathrm{~cm} / \mathrm{s}\) is \(\sqrt{\alpha} \mathrm{cm}\), where \(\alpha=\)____________.JEE Mains 2024 Hard
- Modern vacuum pumps can evacuate a vessel down to a pressure of \(4.0 \times {10^{ - 15}}\, atm\) at room temperature \((300\, K)\). Taking \(R = 8.0\, JK^{-1}\, mole^{-1}\) , \(1\, atm = 10^5\, Pa\) and \(N_ {Avogadro} = 6 \times 10^{23}\, mole^{-1}\) , the mean distance between molecules of gas in an evacuated vessel will be of the order ofJEE Mains 2014 Medium
- The electric field of an electromagnetic wave in free space is represented as \(\vec{E}=E_0 \cos (\omega t-k z) \hat{i}\). The corresponding magnetic induction vector will be _______.JEE Mains 2024 Hard
- An electron moves through a uniform magnetic field \(\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T\). At a particular instant of time, the velocity of electron is \(\overrightarrow{\mathrm{u}}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}\). If the magnetic force acting on electron is \(\vec{F}=5 e\hat kN\), where \(e\) is the charge of electron, then the value of \(\mathrm{B}_0\) is _______\(\mathrm{T}\).JEE Mains 2024 Hard
- When two resistance \(R_1\) and \(R_2\) connected in series and introduced into the left gap of a meter bridge and a resistance of \(10 \Omega\) is introduced into the right gap, a null point is found at \(60 cm\) from left side. When \(R_1\) and \(R_2\) are connected in parallel and introduced into the left gap, a resistance of \(3 \Omega\) is introduced into the right-gap to get null point at 40 cm from left end. The product of \(R_1 R_2\) is \(.............\Omega\)JEE Mains 2023 Hard
- The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case ofJEE Mains 2025 Medium