In some older textbooks

PHYSICS · Multi-part · CBSE · Physics · Light — Reflection and Refraction · Light — Reflection and Refraction

Problem

In some older textbooks, the distances in mirror problems were measured using a left-hand sign rule in which the direction of incident light was taken as negative. Modern textbooks use the Cartesian convention in which the direction of incident light is taken as positive. Consider a concave mirror experiment described below and answer the questions. A real object is placed

24\,\text{cm}

in front of a concave mirror of radius of curvature

36\,\text{cm}

. (i) Using the left-hand sign rule, write the numerical values with proper signs for

u

f

and calculate the image distance

v_{\text{LH}}

. (ii) Convert the same numerical situation to the Cartesian convention and calculate the image distance

v_{\text{C}}

. (iii) Establish an algebraic relationship connecting

v_{\text{LH}}

and

v_{\text{C}}

for any spherical mirror when switching between the two conventions, and verify that your two numerical answers satisfy it.

Related theory

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