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A capillary tube is made of glass of ref...

A capillary tube is made of glass of refractive index `n'`. The outer radius of the tube is `R`. The tube is filled with a liquid of refractive index `n lt n'`. What should be the minimum internal radius of the tube so that any ray that hits the tube would enter the liquid.

A

`(R )/(n)`

B

`(R )/(n')`

C

`(Rn')/(n)`

D

`(Rn)/(n')`

Text Solution

AI Generated Solution

To solve the problem of determining the minimum internal radius of a capillary tube filled with a liquid of refractive index \( n \) (where \( n < n' \), the refractive index of the glass), we need to ensure that any ray of light that hits the tube will enter the liquid. Here’s a step-by-step solution: ### Step 1: Understand the Geometry and Refraction We have a capillary tube made of glass with an outer radius \( R \) and filled with a liquid of refractive index \( n \). We need to determine the minimum internal radius \( r \) of the tube such that any ray of light that strikes the tube will not enter the liquid. ### Step 2: Consider the Limiting Case The critical scenario occurs when the incident ray hits the outer surface of the tube at the steepest angle possible, which is \( 90^\circ \). In this case, the ray will refract into the glass. ...
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