KCET · Physics · Ray Optics
Focal length of a convex lens will be maximum for
- A yellow light
- B green light
- C red light
- D blue light
Answer & Solution
Correct Answer
(C) red light
Step-by-step Solution
Detailed explanation
By lens Maker's formula, focal length of lens is given as
\[
\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)
\]
where, \(\mu\) is refractive index.
\[
\Rightarrow \quad \frac{1}{f} \propto(\mu-1) \Rightarrow f \propto \frac{1}{(\mu-1)}
\]
Since, \(\quad \mu \propto \frac{1}{\lambda}\)
From Eqs. (i) and (ii), we get
\[
f \propto \lambda
\]
But, wavelength of red colour of light is maximum as all the other constituent colours of white light. Hence, focal length of a convex lens is maximum for red light.
\[
\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)
\]
where, \(\mu\) is refractive index.
\[
\Rightarrow \quad \frac{1}{f} \propto(\mu-1) \Rightarrow f \propto \frac{1}{(\mu-1)}
\]
Since, \(\quad \mu \propto \frac{1}{\lambda}\)
From Eqs. (i) and (ii), we get
\[
f \propto \lambda
\]
But, wavelength of red colour of light is maximum as all the other constituent colours of white light. Hence, focal length of a convex lens is maximum for red light.
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