Q8DQ - University Physics with Modern Physics

Question

For a spherical mirror, if s = f , then s' = $\infty$, and the lateral magnification m is infinite. Does this make sense? If so, what does it mean?

Step-by-Step Solution

Answer

Yes, it makes sense that m is infinity and $s\text{'}$ is also infinity.

Step1: Ratio between the distance and the magnification

Now the ratio of between the distance of the object s and the distance of the image s' is called the lateral magnification m and it is given by the equation:

$m=-\frac{s\text{'}}{s}$

Step2: Lateral magnification

Now, it is given that the $s=f$ where f is the focal length and $s\text{'}=\infty$. Putting the values in the above equation we get:

$$\begin{gathered} m=-\frac{s\text{'}}{s} \\ =-\frac{\infty }{f} \\ =\infty \end{gathered}$$

Hence the lateral magnification is given by $\infty$, which makes sense.