A student attempted to find the position and size of the image formed by a concave…

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

Problem

A student attempted to find the position and size of the image formed by a concave mirror for an object placed on the principal axis. The object

AB

of height

2\,\text{cm}

is placed

20\,\text{cm}

in front of the mirror. The focal length of the mirror is

15\,\text{cm}

. The student’s working is reproduced below: Step 1:

u = -20\,\text{cm},\; f = +15\,\text{cm}

Step 2:

\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}

Step 3:

\dfrac{1}{15} = \dfrac{1}{v} - \dfrac{1}{20}

Step 4:

\dfrac{1}{v} = \dfrac{1}{15} + \dfrac{1}{20} = \dfrac{7}{60}

Step 5:

v = 8.57\,\text{cm}

(to two decimal places) Step 6:

m = -\dfrac{v}{u} = -\dfrac{8.57}{-20} = 0.43

Step 7:

h_i = m h_o = 0.43 \times 2 = 0.86\,\text{cm}

(i) Identify any two sign-convention mistakes in the student’s working shown above. (ii) Redo the calculation for

v

m

and

h_i

using the correct signs. (iii) State whether the final image is real or virtual and inverted or erect, giving reason from your corrected values. (iv) Calculate the distance between the object and the image.

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