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

2022 · 25 Jul · Shift 1 · Q56
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. /2022 · 25 Jul · Shift 1 · Q56

Geometrical Optics question

2022 · 25 Jul · Shift 1 · Q56

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
Time taken by light to travel in two different materials AAA and BBB of refractive indices μA\mu_{A}μA​ and μB\mu_{B}μB​ of same thickness is t1t_{1}t1​ and t2t_{2}t2​ respectively. If t2−t1=5×10−10t_{2}-t_{1}=5 \times 10^{-10}t2​−t1​=5×10−10 s and the ratio of μA\mu_{A}μA​ to μB\mu_{B}μB​ is 1:21: 21:2. Then, the thickness of material, in meter is: (Given vAv_{\mathrm{A}}vA​ and vBv_{\mathrm{B}}vB​ are velocities of light in AAA and BBB materials respectively.)
  1. A
    5×10−10 vA m5 \times 10^{-10} \,v_{\mathrm{A}}\, \mathrm{m}5×10−10vA​m
  2. B
    5×10−10 m5 \times 10^{-10} \mathrm{~m}5×10−10 m
  3. C
    1.5×10−10 m1.5 \times 10^{-10} \mathrm{~m}1.5×10−10 m
  4. D
    5×10−10 vB m5 \times 10^{-10} \,v_{\mathrm{B}} \,\mathrm{m}5×10−10vB​m
View written solutionFree

Correct answer: A

  1. Use time taken in a medium

For a slab of thickness ddd, time taken by light is t=dvt=\frac{d}{v}t=vd​ where vvv is the speed of light in that medium.

So for materials AAA and BBB: t1=dvA,t2=dvBt_1=\frac{d}{v_A}, \qquad t_2=\frac{d}{v_B}t1​=vA​d​,t2​=vB​d​

Given: t2−t1=5×10−10 st_2-t_1=5\times 10^{-10}\,\text{s}t2​−t1​=5×10−10s Hence, dvB−dvA=5×10−10\frac{d}{v_B}-\frac{d}{v_A}=5\times 10^{-10}vB​d​−vA​d​=5×10−10

  1. Use refractive index relation

Refractive index is μ=cv⇒v=cμ\mu=\frac{c}{v} \Rightarrow v=\frac{c}{\mu}μ=vc​⇒v=μc​

Given ratio: μA:μB=1:2\mu_A: \mu_B=1:2μA​:μB​=1:2 Since velocity is inversely proportional to refractive index, vA:vB=2:1v_A:v_B=2:1vA​:vB​=2:1 Thus, vA=2vBv_A=2v_BvA​=2vB​

  1. Substitute into the time difference equation

Starting from d(1vB−1vA)=5×10−10d\left(\frac{1}{v_B}-\frac{1}{v_A}\right)=5\times 10^{-10}d(vB​1​−vA​1​)=5×10−10 Using vA=2vBv_A=2v_BvA​=2vB​: d(1vB−12vB)=5×10−10d\left(\frac{1}{v_B}-\frac{1}{2v_B}\right)=5\times 10^{-10}d(vB​1​−2vB​1​)=5×10−10 d(12vB)=5×10−10d\left(\frac{1}{2v_B}\right)=5\times 10^{-10}d(2vB​1​)=5×10−10 d=10−9vBd=10^{-9}v_Bd=10−9vB​

Now since vA=2vBv_A=2v_BvA​=2vB​, we get d=10−9vB=5×10−10(2vB)=5×10−10vAd=10^{-9}v_B=5\times 10^{-10}(2v_B)=5\times 10^{-10}v_Ad=10−9vB​=5×10−10(2vB​)=5×10−10vA​

  1. Match with options

Therefore, thickness is 5×10−10vA m\boxed{5\times 10^{-10}v_A\,\text{m}}5×10−10vA​m​

So the correct option is A.

PreviousNext

More from Geometrical Optics

  • For an object placed at a distance 2.4 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 1.5 and thickness 1 cm is introduced between lens and screen…2022 · MCQ
  • A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from…2022 · Numerical
  • A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the…2022 · MCQ
  • The difference of speed of light in the two media A and B (vA − vB) is 2.6 × 107 m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is : (Given : speed of light in vacuum c…2022 · MCQ
  • The graph between u1​ and v1​ 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 same radius of… Includes diagram2022 · Numerical
  • Light travels in two media M1​ and M2​ with speeds 1.5×108 ms−1 and 2.0×108 ms−1 respectively. The critical angle between them is :2022 · MCQ
  • In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle 60∘ at the side AC, the refractive light beam just grazes along face AC. The refractive index… Includes diagram2022 · Numerical
  • A light ray is incident, at an incident angle θ 1, on the system of tow plane mirrors M1 and M2 having an inclination angle 75 ∘ between them (as shown in figure). After reflecting from mirror M1 it gets reflected back by the… Includes diagram2022 · Numerical