Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Geometrical Optics question

2021 · 16 Mar · Shift 2 · Q47
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Geometrical Optics
  5. /2021 · 16 Mar · Shift 2 · Q47

Geometrical Optics question

2021 · 16 Mar · Shift 2 · Q47

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens are R1 and R2 respectively.
  1. A
    Zero
  2. B
    Infinite
  3. C
    1
  4. D
    R1R2R1−R2{{{R_1}{R_2}} \over {{R_1} - {R_2}}}R1​−R2​R1​R2​​
View written solutionFree

Correct answer: B

  1. Use the lens maker formula in a medium

For a thin lens of refractive index nℓn_\ellnℓ​ placed in a medium of refractive index nmn_mnm​, the focal length is given by

1f=(nℓnm−1)(1R1−1R2).\frac{1}{f} = \left(\frac{n_\ell}{n_m}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right).f1​=(nm​nℓ​​−1)(R1​1​−R2​1​).
  1. Substitute the given condition

Here, the lens is placed in a medium having the same refractive index as the lens. So,

nℓ=nm=1.4.n_\ell = n_m = 1.4.nℓ​=nm​=1.4.

Hence,

nℓnm=1.41.4=1.\frac{n_\ell}{n_m} = \frac{1.4}{1.4} = 1.nm​nℓ​​=1.41.4​=1.

Therefore,

1f=(1−1)(1R1−1R2)=0.\frac{1}{f} = (1-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) = 0.f1​=(1−1)(R1​1​−R2​1​)=0.
  1. Interpret the result

If

1f=0,\frac{1}{f}=0,f1​=0,

then

f=∞.f = \infty.f=∞.

So the lens has no refracting power in a medium of the same refractive index.

  1. Check the options
  • A: Zero →\rightarrow→ incorrect
  • B: Infinite →\rightarrow→ correct
  • C: 1 →\rightarrow→ incorrect
  • D: R1R2R1−R2\dfrac{R_1R_2}{R_1-R_2}R1​−R2​R1​R2​​ →\rightarrow→ incorrect

Final Answer

B: Infinite\boxed{\text{B: Infinite}}B: Infinite​
PreviousNext

More from Geometrical Optics

  • Red light differs from blue light as they have :2021 · MCQ
  • A deviation of 2 ∘ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as 0.02 and 0.03 respectively and refractive index for yellow light…2021 · Numerical
  • The thickness at the centre of a plane convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 × 108 ms − 1. The focal length of the lens is ​.2021 · MCQ
  • The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at 32rd​ of the distance of the object from the surface. The wavelength of…2021 · Numerical
  • Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as :2021 · MCQ
  • Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in the figure. The refractive indices of the material of the prism for red, green and blue wavelength are 1.27,… Includes diagram2021 · MCQ
  • Region I and II are separated by a spherical surface of radius 25 cm. An object is kept in region I at a distance of 40 cm from the surface. The distance of the image from the surface is : Includes diagram2021 · MCQ
  • An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an…2021 · Numerical