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Geometrical Optics question

2021 · 24 Feb · Shift 1 · Q52
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  5. /2021 · 24 Feb · Shift 1 · Q52

Geometrical Optics question

2021 · 24 Feb · Shift 1 · Q52

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
The focal length f is related to the radius of curvature r of the spherical convex mirror by :
  1. A
    f = r
  2. B
    f = −-− r
  3. C
    f = +12{{1 \over 2}}21​ r
  4. D
    f = −12-{{1 \over 2}}−21​ r
View written solutionFree

Correct answer: C

  1. Use the mirror formula relation between focal length and radius of curvature

For any spherical mirror,

f=R2f = \frac{R}{2}f=2R​

where RRR is the radius of curvature.

  1. Apply sign convention for a convex mirror

For a convex mirror, both the focus and center of curvature lie behind the mirror. So, under the Cartesian sign convention:

  • Radius of curvature R>0R > 0R>0
  • Focal length f>0f > 0f>0

Thus,

f=+r2f = +\frac{r}{2}f=+2r​

  1. Match with the given options

The correct option is:

f=+12rf = +\frac{1}{2}rf=+21​r

So, Option C is correct.

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