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NCERT Exemplar · Class 12 · Physics

Chapter 9: Ray Optics and Optical Instruments

Practice each question, then open the answer or worked solution.

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Questions

32 questions
Q9.31Written answer

An infinitely long cylinder of radius R is made of an unusual exotic material with refractive index –1. The cylinder is placed between two planes whose normals are along the y-direction. The centre of cylinder O lies along the y-axis. A narrow laser beam is directed along the y-direction from the lower plate. The laser source is at a horizontal distance x from the diameter in the y-direction. Find the range of x such that light emitted from the lower plane does not reach the upper plane.

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Worked solution

The refractive index of the cylinder is -1 and is placed in the air of μ = 1

AB is incident at B to the cylinder such that θr will be negative

θ1= θi = θr

The total deviation of the outcoming ray is 4θ1.

When the angles are measured clockwise, the planes π/3 ≤ 4θ ≤ 3 π/2

If the plane is at R π/r ≤ x ≤ 3R π/8, the light emitted from the source shall not reach the plane.

Q9.32Written answer

(i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as 2 0 () – α = b wb w, where b is the verticle distance from the pole. w0 is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.

ii) A gravitational lens may be assumed to have a varying width of the form w(b) = k1 ln (k2/b) = k1 ln (k2/bmin). Show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius.

β = √(n-1)k1 u/v / u + v

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Worked solution

i) Time taken by the ray to travel from S to P1 is = t1 = √u2 + b2/c

Time taken by the ray to travel from P1 to O is = t2 = v/c (1+ ½ b2/v2)

Time taken to travel through the lens is = tl = (n – 1)w(b)/c

Total time is = t = 1/c (u + v + ½ b2/D + (n – 1)(wo + b2/a))

D is the focal length as 1/D = 1/u + 1/v

ii) Differentiating the expression for time, we get

β = b/v = √(n-1)k1u/(u + v)v

Optical instruments are the tools with which different calculations and measurements of light take place. The ray in optics is used for light propagation and highlighting the path along which the light gets propagated through a medium.

Some of the major terminology explained in this chapter are given below:

  1. Refraction
  2. Incident Ray and Refracted
  3. Laws of Reflection and Refraction
  4. Refractive Index
  5. Convex and Concave Mirrors
  6. Transparent and Translucent Medium
  7. Focal Plane, Focal Length and Principal Focus

To learn more about the NCERT Exemplar Solutions for Class 12 Physics Chapter 9 Ray Optics and Optical Instruments, download the PDF available below: