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GUJCET · Physics · Ray Optics and Optical Instruments
A ray coming from an object which is situated at \(O\) distance in the air and falls on a spherical glass surface ( \(n=1.5\) ) Then the distance of the image will be ________ . \(R\) is the radius of curvature of a spherical glass.
- A 2 R
- B R
- C 3 R
- D 1.5 R
Answer & Solution
Correct Answer
(C) 3 R
Step-by-step Solution
Detailed explanation
(C) 3 R
\(\frac{n_{2}}{\mathrm{v}}-\frac{n_{1}}{u}=\frac{n_{2}-n_{1}}{\mathrm{R}}\)
\(
\begin{aligned}
\frac{1.5}{v}-\frac{1}{\infty} & =\frac{1.5-1}{R} \\
\frac{1.5}{v} & =\frac{0.5}{R} \\
& \left(\because \frac{1}{\infty}=0\right) \\
v & =\frac{1.5 \mathrm{R}}{0.5} \\
v & =3 \mathrm{R}
\end{aligned}
\)
\(\frac{n_{2}}{\mathrm{v}}-\frac{n_{1}}{u}=\frac{n_{2}-n_{1}}{\mathrm{R}}\)
\(
\begin{aligned}
\frac{1.5}{v}-\frac{1}{\infty} & =\frac{1.5-1}{R} \\
\frac{1.5}{v} & =\frac{0.5}{R} \\
& \left(\because \frac{1}{\infty}=0\right) \\
v & =\frac{1.5 \mathrm{R}}{0.5} \\
v & =3 \mathrm{R}
\end{aligned}
\)
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