✓ Board-verified
Physics · 2026 · 2 marks
Ray Optics and Optical InstrumentsReflection of Light by Spherical Mirrors2 marksApplyvery short answer
CBSE 2026 · Region 2 · Set 1 · Q21
A 5 cm long pencil is placed along the principal axis of a concave mirror of focal length 20 cm such that its nearest end is at a distance of 25 cm…
A $\displaystyle 5$ cm long pencil is placed along the principal axis of a concave mirror of focal length $\displaystyle 20$ cm such that its nearest end is at a distance of $\displaystyle 25$ cm from the mirror. Calculate the length of the image of the pencil.
OR In a Young's double-slit experiment, a beam of light consisting of two wavelengths $\displaystyle 500$ nm and $\displaystyle 600$ nm is used. The interference fringes are observed at a screen placed $\displaystyle 1.8$ m away from the plane of slits (slit separation $\displaystyle 0.3$ mm). Calculate the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.
Marking-scheme solution
$\displaystyle \dfrac{1}{\mathrm{f}}=\dfrac{1}{\mathrm{v}}+\dfrac{1}{u}$
$\displaystyle \dfrac{1}{v_{1}}=\dfrac{1}{\mathrm{f}}-\dfrac{1}{u_{1}}=\dfrac{1}{(-20)}-\dfrac{1}{(-25)}$ (For near end of the pencil)
$\displaystyle v_{1}=-100 \mathrm{~cm}$
$\displaystyle \dfrac{1}{v_{2}}=\dfrac{1}{(-20)}-\dfrac{1}{(-30)}$ (For far end of the pencil)
$\displaystyle v_{2}=-60 \mathrm{~cm}$
Length of the image $\displaystyle \mathrm{L}=\left|v_{1}\right|-\left|v_{2}\right|=40 \mathrm{~cm}$
$\displaystyle n_{1} \lambda_{1}=n_{2} \lambda_{2}$
$\displaystyle \dfrac{n_{1}}{n_{2}}=\dfrac{\lambda_{2}}{\lambda_{1}}=\dfrac{600}{500}=\dfrac{6}{5}$
$\displaystyle y_{6}^{\max }=n_{1} \dfrac{\lambda_{1} D}{d}=\dfrac{6 \times 500 \times 10^{-9} \times 1.8}{0.3 \times 10^{-3}}$
$\displaystyle =18 \mathrm{~mm}$
Alternatively: $\displaystyle n \lambda_{1}=(n+1) \lambda_{2}$, we get $\displaystyle n=5$
$\displaystyle y_{5}^{\max }=\dfrac{n_{2} \lambda_{2} \mathrm{D}}{d}=\dfrac{5 \times 600 \times 10^{-9} \times 1.8}{0.3 \times 10^{-3}}=18 \mathrm{~mm}$
All Ray Optics and Optical Instruments questions2026 question paperNCERT solutions: Ray Optics and Optical InstrumentsPractice Ray Optics and Optical Instruments →
More from Ray Optics and Optical Instruments
- A small bulb is placed at the bottom of a tank, containing a transparent liquid of refractive index √2, to a depth of 1 m. Calculate the area of the…2026
- Assertion: A convex lens, when immersed in a liquid, disappears. Reason ( R ): The refractive indices of material of the lens and the liquid are…2024
- A right angled isosceles glass prism ABC is kept in contact with an equilateral triangular prism DBC as shown in the figure. Both prisms are made of…2025
- A convex lens (n = 1.52) has a focal length of 15.0 cm in air. Find its focal length when it is immersed in liquid of refractive index 1.65. What…2024
- (i) Draw a labelled ray diagram showing the formation of the image at infinity by an astronomical telescope. (ii) A telescope consists of an…2022
- Two convex lenses A and B, each of focal length 10.0 cm, are mounted on an optical bench at 50.0 cm and 70.0 cm respectively. An object is mounted at…2025
- A right-angled prism ABC (refractive index √2 ) is kept on a plane mirror as shown in the figure. A ray of light is incident normally on the face AC.…2025
- A ray of light is incident on a glass prism of refractive index μ and refracting angle A. If it just suffers total internal reflection at the other…2023
CBSE Class 12 Physics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.