Question:
The graph between \(\frac 1u\) and \(\frac 1v\) for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5, and its both the surfaces have the same radius of curvature R. The value of R will be______cm.
(where u = object distance, v = image distance)
The graph between \(\frac 1u\) and \(\frac 1v\) for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5, and its both the surfaces have the same radius of curvature R. The value of R will be______cm.
(where u = object distance, v = image distance)
(where u = object distance, v = image distance)
Updated On: Jul 8, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 10
Solution and Explanation
Focus \(f=10\ cm\)
\(\frac 1f=(μ−1)(\frac 1R−\frac {1}{−R})\)
\(\frac {1}{10}=\frac {1.5−1}{1}×\frac 2R\)
\(\frac {1}{10}=\frac {0.5×2}{R}\)
\(\frac {1}{10}=\frac 1R\)
\(R=10\ cm\)
So, the answer is \(10\ cm.\)
Was this answer helpful?
2
0
Top JEE Main Physics Questions
- In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and 50th division of circular scale coincides with the reference line of main scale. The diameter of sphere is _______ mm.}
- JEE Main - 2026
- Physics
- Units, Dimensions and Measurements
- 1 mole of ideal diatomic gas is enclosed in a cylinder piston arrangement having cross-sectional area of piston \(4\,\text{cm}^2\). If gas has only rotational modes and \(P_{atm}=100\ \text{kPa}\), some amount of heat is added to the system as a result piston moves up slowly by \(2.5\,\text{cm}\). If temperature change is \(1.2^\circ C\). Find heat given to gas.
- JEE Main - 2026
- Physics
- Thermal Physics
Refer the figure below. \( \mu_1 \) and \( \mu_2 \) are refractive indices of air and lens material respectively. The height of image will be _____ cm.
- JEE Main - 2026
- Physics
- Optics and Refraction
In single slit diffraction pattern, the wavelength of light used is \(628\) nm and slit width is \(0.2\) mm. The angular width of central maximum is \(\alpha \times 10^{-2}\) degrees. The value of \(\alpha\) is ____.
- JEE Main - 2026
- Physics
- Interference and Diffraction
- If X and Y are the inputs, the given circuit works as _______.
- JEE Main - 2026
- Physics
- Digital Circuits
View More Questions
Top JEE Main spherical lenses Questions
- A spherical interface lens of radius $R$ separates two media of refractive indices $1$ and $1.4$ respectively as shown in the figure below. A point source is placed at a distance of $4R$ in front of spherical interface. The magnitude of the magnification of point source image is ————.
- JEE Main - 2026
- Physics
- spherical lenses
- Radius of curvature of equiconvex lens is 20 cm. Material of lens is having refractive index of 1.5. Find image distance from lens if an object is placed 10 cm away from the lens.
- JEE Main - 2024
- Physics
- spherical lenses
- A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:
- JEE Main - 2024
- Physics
- spherical lenses
- For an object placed at a distance $24\, m$ from a lens, a sharp focused image is observed on a screen placed at a distance $12\, cm$ from the lens A glass plate of refractive index $15$ and thickness $1 \,cm$ is introduced between lens and screen such that the glass plate plane faces parallel to the screen By what distance should the object be shifted so that a sharp focused image is observed again on the screen?
- JEE Main - 2023
- Physics
- spherical lenses
Two objects \(A\) and \(B\)are placed at \(15\, cm\) and \(25\, cm\) from the pole in front of a concave mirros having radius of curvature \(40\, cm\). The distance between images formed by the mirror is:
- JEE Main - 2023
- Physics
- spherical lenses
View More Questions
Top JEE Main Questions
- In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and 50th division of circular scale coincides with the reference line of main scale. The diameter of sphere is _______ mm.}
- JEE Main - 2026
- Units, Dimensions and Measurements
- A D-aldotetrose on oxidation with concentrated \(HNO_3\) resulted in optically inactive dicarboxylic acid. The structure of the D-aldotetrose is:
- JEE Main - 2026
- Carbohydrates
- Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure.
Statement II: In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas.
In the light of the above statements, choose the correct answer:- JEE Main - 2026
- The Kinetic Theory of Gases
- 1 mole of ideal diatomic gas is enclosed in a cylinder piston arrangement having cross-sectional area of piston \(4\,\text{cm}^2\). If gas has only rotational modes and \(P_{atm}=100\ \text{kPa}\), some amount of heat is added to the system as a result piston moves up slowly by \(2.5\,\text{cm}\). If temperature change is \(1.2^\circ C\). Find heat given to gas.
- JEE Main - 2026
- Thermal Physics
- Let $S = \{\theta \in (-2\pi, 2\pi) : \cos\theta + 1 = \sqrt{3} \sin\theta\}$. Then $\sum_{\theta \in S} \theta$ is equal to:
- JEE Main - 2026
- Trigonometry
View More Questions
Concepts Used:
Spherical Lenses
Lenses that are made by combining two spherical transparent surfaces are called spherical lenses. In general, there are two kinds of spherical lenses. Lenses that are made by joining two spherical surfaces that bulge outward are convex lenses, whereas lenses that are made by joining two spherical surfaces that curve inward are concave lenses.
Properties of Convex lens:
- In this, the lenses are thicker in the middle and thinner at the edges.
- They have a positive focal length.
- It intersects the incident rays towards the principal axis
- These lenses are used in the camera, focus sunlight, projector microscope, simple telescope, overhead projector, magnifying glasses, etc.
Properties of Concave lens:
- These lenses are thinner in the middle and thicker at the edges.
- They have a negative focal length.
- It parts the incident rays away from the principal axis.
- These are used in the glasses, spy holes, some telescopes in the doors, etc.