Question

Inside a substance such as glass or water, light travelss more slowly than it does in a vacuum. If $c$ denotes
the speed of light in a vacuum and $v$ denotes its speed through some other substance, then $v=\frac{c}{n}$ Where $n$ is a constant called the index of refraction.
To almost exact approximation, a substance's index of refraction does not depend the wavelength of light. For instance, when red and blue light waves enter water, they both slow down by about the same amount. More precise measurements, however, reveal that n varies with wavelength. Table 1 presents some indices of refraction of Cutson glass, for different wavelengths of visible light. A nanometer (nm) is $10^{-9}$ meters. In a vacuum, light travesl at $c=3.0\times 10^{8}m/s$.

Indices of refraction of Cutson glass (Table 1)

Approximate	Wavelength in vacuum (nm)	n
Yellow	580	1.500
Yellow orange	600	1.498
Orange	620	1.496
Orange red	640	1.494

A concave mirror is placed over a beaker containing water of $\mu =1.33$ and image of the object placed at the bottom of the beaker is formed at a distance 25 $cm$ from the top, then the focal length of the mirror is:

• A. $10cm$
• B. $15cm$
• C. $20cm$
• D. $25cm$

Answer 1

Answer: (C)

After refraction from the top surface of water the image of the object is formed at a distance h from the top surface of water.
Thus, $h=\frac{33.25}{1.33}=25cm$
Now for the concave mirror
$u=25+15=40cm$
For the second refraction, the position of the image is $h^{\prime }=\frac{25}{1.33}=18.8cm$
The image distance $v$ from the concave mirror is therefore
$v=15+18.8=33.8cm$
Using mirror formula, its focal length $f$ is
$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
$\frac{1}{f}=\frac{1}{40}+\frac{1}{33.8}$
or $f=18.31cm$
The nearest answer is therefore $20cm$