While determining the final image formed by a two–mirror system

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Geometric Optics · Geometric Optics

Problem

While determining the final image formed by a two–mirror system, a student produced the following working: Step 1: For a first concave mirror of focal length

f_{1}= -12\,\text{cm}

and object distance

u_{1}=-18\,\text{cm}

, the student wrote

\frac{1}{v_{1}}+\frac{1}{(-18)}=\frac{1}{-12},\qquad v_{1}=7.2\,\text{cm}.

Step 2: The image from Step 1 acts as an object for a second convex mirror of focal length

f_{2}= +20\,\text{cm}

placed

40\,\text{cm}

to the right of the first mirror. The student treated the object distance for the second mirror as

u_{2}=+32.8\,\text{cm}

and found

\frac{1}{v_{2}}+\frac{1}{(+32.8)}=\frac{1}{+20},\qquad v_{2}=55\,\text{cm}.

Answer the following questions based on the above working. (i) Locate and explain every inconsistency, if any, in the signs taken for

v_{1}

and

u_{2}

according to the Cartesian convention. (ii) Correct the sign(s) and recalculate

v_{1}

and

v_{2}

. (iii) State clearly where the final image is formed with respect to the second mirror and comment on its nature (real/virtual, erect/inverted).

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