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The following letter may be of general interest:

Respected Sir,

I have a confusion about the topic optics. I am very confused about the sign convention used in solving lens problems or spherical mirror problems. Please aware me what is the true sign convention to be used.

Thanking you ...

Answer: There are two kinds of sign conventions:

1. Real-Virtual.
2. Co-ordinate.

Both are correct and can be used. However, co-ordinate sign convention is found easy by most and therefore is recommended.

### A man starts walking from the point P (-3, 4) ....

A man starts walking from the point P (-3, 4), touches the x-axis at R, and then turns to reach at the point Q (0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $50 [(PR)^2 + (RQ)^2 ]$ is equal to _ _ _ _ . Solution For time to be minimum at constant speed, the directions must be symmetric. In other words, the angles made by PR and RQ with the vertical must be the same just like in the law of reflection in optics. $tan \theta = \frac {MP}{MR} = \frac {NQ}{NR}$ $\Rightarrow \frac {3-r}{4} = \frac {r}{2}$ $\Rightarrow r=1$ So, $R \equiv ( - 1,0)$ Now, $50(PR^2+RQ^2)=50[(4+16)+(1+4)]=1250$