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

2011 · Shift 0 · Q57
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. /2011 · Shift 0 · Q57

Geometrical Optics question

2011 · Shift 0 · Q57

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
Let xxx-zzz plane be the boundary between two transparent media. Medium 111 in z≥0z \ge 0z≥0 has a refractive index of 2\sqrt 22​ and medium 222 with z<0z \lt 0z<0 has a refractive index of 3.\sqrt 3 .3​. A ray of light in medium 111 given by the vector A→=63i^+83j^−10k^\overrightarrow A = 6\sqrt 3 \widehat i + 8\sqrt 3 \widehat j - 10\widehat kA=63​i+83​j​−10k is incident on the plane of separation. The angle of refraction in medium 222 is:
  1. A
    45∘{45^ \circ }45∘
  2. B
    60∘{60^ \circ }60∘
  3. C
    75∘{75^ \circ }75∘
  4. D
    30∘{30^ \circ }30∘
View written solutionFree

Correct answer: NONE OF THE OPTIONS; IF THE QUESTION DATA ARE EXACTLY AS GIVEN, THE REFRACTED ANGLE IS ABOUT 36°

  1. Identify the interface and the normal

The boundary is the xxx-zzz plane, i.e. y=0y=0y=0. So the normal to the plane is along the yyy-axis.

Since the ray is going toward the plane from medium 111 (z≥0(z\ge 0(z≥0 is irrelevant here; the boundary is y=0y=0y=0), we use the angle made with the normal j^\hat{j}j^​.

  1. Given incident ray vector
A⃗=63 i^+83 j^−10 k^\vec A = 6\sqrt{3}\,\hat i + 8\sqrt{3}\,\hat j - 10\,\hat kA=63​i^+83​j^​−10k^

Its magnitude is

∣A⃗∣=(63)2+(83)2+(−10)2|\vec A| = \sqrt{(6\sqrt3)^2 + (8\sqrt3)^2 + (-10)^2}∣A∣=(63​)2+(83​)2+(−10)2​ =108+192+100=400=20= \sqrt{108 + 192 + 100} = \sqrt{400} = 20=108+192+100​=400​=20
  1. Find the angle of incidence

The angle of incidence iii is the angle between the ray and the normal to the surface.

The normal is along j^\hat jj^​, so

cos⁡i=∣Ay∣∣A⃗∣=8320=235\cos i = \frac{|A_y|}{|\vec A|} = \frac{8\sqrt3}{20} = \frac{2\sqrt3}{5}cosi=∣A∣∣Ay​∣​=2083​​=523​​

Hence,

sin⁡i=1−cos⁡2i\sin i = \sqrt{1-\cos^2 i}sini=1−cos2i​ =1−(235)2=1−1225=1325=135= \sqrt{1-\left(\frac{2\sqrt3}{5}\right)^2} = \sqrt{1-\frac{12}{25}} = \sqrt{\frac{13}{25}} = \frac{\sqrt{13}}{5}=1−(523​​)2​=1−2512​​=2513​​=513​​
  1. Apply Snell's law

Given:

n1=2,n2=3n_1 = \sqrt2, \qquad n_2 = \sqrt3n1​=2​,n2​=3​

Snell's law:

n1sin⁡i=n2sin⁡rn_1 \sin i = n_2 \sin rn1​sini=n2​sinr

So,

sin⁡r=n1n2sin⁡i=23⋅135\sin r = \frac{n_1}{n_2}\sin i = \frac{\sqrt2}{\sqrt3}\cdot \frac{\sqrt{13}}{5}sinr=n2​n1​​sini=3​2​​⋅513​​ =2653= \frac{\sqrt{26}}{5\sqrt3}=53​26​​

This gives

sin⁡r≈0.589\sin r \approx 0.589sinr≈0.589

Therefore,

r≈36∘r \approx 36^\circr≈36∘
  1. Compare with the options

The computed refracted angle is approximately 36∘36^\circ36∘, which does not match any of the given options 30∘,45∘,60∘,75∘30^\circ, 45^\circ, 60^\circ, 75^\circ30∘,45∘,60∘,75∘.

So the data in the question appears inconsistent.

  1. Comparison with stored answer

Stored correct answer is A: 45∘45^\circ45∘.

But from the given vector and the stated boundary plane, the refracted angle is not 45∘45^\circ45∘.

Hence I do not agree with the stored answer.

PreviousNext

More from Geometrical Optics

  • An initially parallel cylindrical beam travels in a medium of refractive index μ(I)=μ0​+μ2​I, where μ0​ and μ2​ are positive constants and I is the intensity of the light beam. The…2010 · MCQ
  • An initially parallel cylindrical beam travels in a medium of refractive index μ(I)=μ0​+μ2​I, where μ0​ and μ2​ are positive constants and I is the intensity of the light beam. The…2010 · MCQ
  • A transparent solid cylindrical rod has a refractive index of 3​2​. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle θ for which the… Includes diagram2009 · MCQ
  • In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and…2009 · MCQ
  • A student measures the focal length of a convex lens by putting an object pin at a distance ′u′ from the lens and measuring the distance ′v′ of the image pin. The graph between ′u′ and ′v′ plotted by the student should look like2008 · MCQ
  • Two lenses of power −15D and +5D are in contact with each other. The focal length of the combination is2007 · MCQ
  • The refractive index of a glass is 1.520 for red light and 1.525 for blue light. Let D1​ and D2​ be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then,2006 · MCQ
  • A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 34​ and the fish is 12cm below the surface, the radius of this circle in cm is2005 · MCQ