Question

The speed of light in water is ${\left( {\dfrac{3}{4}} \right)^{th}}$ of that in air. If the wavelength of the same light in air is $6000\mathop A\limits^o $ , its wavelength in air is
A. $6000\mathop A\limits^o $
B. $6500\mathop A\limits^o $
C. $4000\mathop A\limits^o $
D. $4500\mathop A\limits^o $

Answer 1

Hint: Recall which property of light remains same when speed changes. Think about which quantity is responsible for the change in speed of light in other mediums. Since the other quantity remains unchanged, the speed of light will be directly proportional to the variable quantity.

Complete step by step answer:
The frequency of light remains the same when light moves from one medium to another.
We know that speed is equal to the product of wavelength and frequency.
Therefore,
$v = \lambda \nu $
Where $v$ is the velocity of light, $\lambda $ is the wavelength and $\nu $ is the frequency of light.
Since the speed changes when light moves from one medium to another and the frequency remains constant, thus the wavelength must change.
Speed is directly proportional to wavelength.
Thus when speed decreases by ${\left( {\dfrac{3}{4}} \right)^{th}}$ the wavelength also decreases by ${\left( {\dfrac{3}{4}} \right)^{th}}$ .
Given, that the wavelength of light in air $ = 6000\mathop A\limits^o $
Thus the wavelength in water is ${\left( {\dfrac{3}{4}} \right)^{th}}$ of the wavelength in air.
Hence wavelength in water
$
   \Rightarrow \lambda = \dfrac{3}{4} \times 6000 \\
   \Rightarrow \lambda = 4500\mathop A\limits^o \\
 $

So, the correct answer is “Option D”.

Additional Information:
The speed of light is the distance travelled by light per unit time.
Frequency is the number of vibrations per unit time. It is just the inverse of time periods. Its unit is Hertz.
Wavelength is the distance between two adjacent crests or two adjacent troughs. Its unit is meter.

Note:
Many students are confused about which property among wavelength and frequency changes. Students should know the fact that the frequency of light remains unchanged when light moves from one medium to another medium. Also the wavelength changes in change of medium and due to this the speed of light changes.