The figure shows cross section of a hollow glass tube of internal radius $r$ , external radius $R$ and index of refraction $n$ . For two rays DE and ABC (in which DE lies on ODE and DE is parallel to BC), the separation $r_{1}$ will be :

r_{1} = (n - 1) R

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r_{1} = n^{2} R

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r_{1} = n r

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

r_{1} = n^{2} r

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $r_{1} = n r$

In given figure $θ$ is angle of refraction and $α$ is angle of incidence for ray ABC.

Required length = $r_{1} = B P$

Since $D E ∥ B C ⟹ ∠ B O P = θ$

Now, in $Δ B O P : -$

$r_{1} = B P = O B sin θ = R sin θ$

$⟹ sin θ = \frac{r_{1}}{R}$

In $Δ O A B : -$
$∠ A = 90^{o}$
$sin α = \frac{r}{R}$

Now, at refraction of ray $A B C$

$\frac{sin θ}{sin α} = n$

$⟹ \frac{r_{1} / R}{r / R} = n ⟹ \frac{r_{1}}{r} = n$

$⟹ r_{1} = n r$

Answer-(C)

Suggest Corrections

Similar questions

Q. The emf (V) and internal resistance (

r

) of a single battery which is equivalent to a parallel combination of two batteries of emf's

V_{1}

and

V_{2}

and internal resistance

r_{1}

and

r_{2}

, respectively, with polarities as shown in the figure are given by

\frac{V_{1} r_{2} - V_{2} r_{1}}{r_{1} + r_{2}}, \frac{r_{1} r_{2}}{r_{1} + r_{2}}

Q. Two cells of same emf are in series with an external resistance R. The internal resistance

r_{1}

r_{2}

. The p.d across the

1^{s t}

cell is found to be zero the value of R is

If the area of a circle with radius r is equal to the curved surface area of cone with radius $r_{1}$ and slant height l then the value of $r_{1}$ in terms of r and l is:

Q. Two resistors of resistance

R_{1}

and

R_{2}

having

R_{1} > R_{2}

are connected in parallel. For equivalent resistance R, the correct statement is

If the area of a circle with radius $r$ is equal to the curved surface area of cone with radius $r_{1}$ and slant height $l$ then the value of $r_{1}$ in terms of $r$ and $l$ is:

Join BYJU'S Learning Program

The figure shows cross section of a hollow glass tube of internal radius r, external radius R and index of refraction n. For two rays DE and ABC (in which DE lies on ODE and DE is parallel to BC), the separation r1 will be :

The figure shows cross section of a hollow glass tube of internal radius $r$ , external radius $R$ and index of refraction $n$ . For two rays DE and ABC (in which DE lies on ODE and DE is parallel to BC), the separation $r_{1}$ will be :