Optics Ques 215
- The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea $(7.8 $ $mm)$. This surface separates two media of refractive indices $1$ and $1.34$. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.
(2019 Main, 10 Jan II)
(a) $4.0 $ $cm$
(b) $2 $ $cm$
(c) $3.1 $ $cm$
(d) $1 $ $cm$
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Answer:
Correct Answer: 215.(c)
Solution:
Formula:
Refraction at Spherical Surfaces:
- The given condition is shown in the figure below
where, a parallel beam of light is coming from air $(\mu=1)$ to a spherical surface (eye) of refractive index $1.34$.
Radius of curvature of this surface is $7.8$ $ mm$.
From the image formation formula for spherical surface, i.e. relation between object, image and radius of curvature.
$ \frac{\mu _r}{v}-\frac{\mu _i}{u}=\frac{\mu _r-\mu _i}{R} $
Given, $\mu _r=1.34, \mu _i=1, u=\infty(-ve)$ and
$ R=7.8 $
Substituting the given values, we get
$\frac{1.34}{v}+\frac{1}{\infty} =\frac{1.34-1}{7.8} $
$\text { or } \frac{1.34}{v} =\frac{0.34}{7.8} $
$\Rightarrow v =\frac{1.34 \times 7.8}{0.34}$ $ mm $
$\Rightarrow v =\frac{4}{3} \times 3 \times 7.8 $ $mm$
$(\because$ approximately $1.34=4 / 3$ and $0.34=1 / 3)$
$\Rightarrow$ $ v=31.2$ $ mm \text { or } 3.12$ $ cm $
BETA
