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Geometrical Optics question

2007 · Shift 1 · Q65
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  5. /2007 · Shift 1 · Q65

Geometrical Optics question

2007 · Shift 1 · Q65

JEE AdvancedPhysicsGeometrical OpticsMCQ+3 / −1
Statement 1 : The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature. Statement 2 : Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.
  1. A
    Statement 1 is True, Statement 2 is True, Statement 2 is a CORRECT explanation for Statement 1
  2. B
    Statement 1 is True, Statement 2 is True, Statement 2 is NOT a CORRECT explanation for Statement 1
  3. C
    Statement 1 is True, Statement 2 is False
  4. D
    Statement 1 is False, Statement 2 is True
View written solutionFree

Correct answer: C

  1. Interpret Statement 1

For a spherical mirror, the mirror formula is

1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}f1​=v1​+u1​

This formula is derived under the paraxial approximation, i.e. for rays close to the principal axis and for a mirror aperture small compared to its radius of curvature.

So, the statement that the formula is valid only for mirrors whose sizes are very small compared to their radii of curvature is essentially true in the JEE context.

Thus, Statement 1 is True.

  1. Interpret Statement 2

The laws of reflection are:

  • Angle of incidence equals angle of reflection
  • Incident ray, reflected ray, and normal lie in the same plane

These laws are valid at every point of any reflecting surface, whether plane or curved, provided we consider the local normal at the point of incidence.

So they are not restricted to plane surfaces. They are valid for spherical mirrors as well.

Hence, Statement 2 is False.

  1. Match with options
  • A: Both true, and 2 explains 1 — incorrect
  • B: Both true, but 2 does not explain 1 — incorrect
  • C: Statement 1 true, Statement 2 false — correct
  • D: Statement 1 false, Statement 2 true — incorrect
  1. Final conclusion

The correct option is:

C\boxed{\text{C}}C​
  1. Comparison with stored answer

Stored correct answer: C

My derived answer: C

So, they agree.

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