List - 1 gives different lens configurations. Radius of curvature of each surface is depicted in figure. Refractive index of glass of lens is $\frac{3}{2}$ and medium in which it is placed is 1. Rays of light parallel to axis of lens from left passes through lens and get focussed at distance 'x' from lens. List - 2 gives value of 'x', then correct match is

I \to P, I I \to P, I I I \to R, I V \to R

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

I \to P, I I \to R, I I I \to P, I V \to R

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

I \to R, I I \to R, I I I \to P, I V \to P

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

I \to P, I I \to S, I I I \to R, I V \to R

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

Open in App

Solution

The correct option is A $I \to P, I I \to P, I I I \to R, I V \to R$
For a convex lens, $R_{1}$ is taken as positive and $R_{2}$ is taken as negative. For a concave lens, $R_{1}$ is taken as negative and $R_{2}$ is taken as positive.
By lens formula $\Rightarrow \frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

I) $\frac{1}{f} = (\frac{3}{2} - 1) (\frac{1}{R} + \frac{2}{R}) \Rightarrow f = x = \frac{2 R}{3}$

II) $\frac{1}{f} = (\frac{3}{2} - 1) (\frac{- 2}{R} - \frac{1}{R}) \Rightarrow f = x = - \frac{2 R}{3}$

III) $\frac{1}{f} = (\frac{3}{2} - 1) (\frac{1}{\infty} - \frac{1}{R}) \Rightarrow f = x = - 2 R$

IV) $\frac{1}{f} = (\frac{3}{2} - 1) (\frac{2}{R} - \frac{1}{R}) \Rightarrow f = x = 2 R$

Suggest Corrections

Similar questions

Q. The radius of curvature of the face of a plano-convex lens silvered from the plane surface is 12cm and its refractive index is 1.5. At what distance from the lens the parallel rays incident on the convex face will converge?

Q. A lens is made up of two identical spherical surfaces having radius of curvature and refractive index

20 cm

and

1

respectively. If the lens is placed in a medium having refractive index

2

, what will be the nature of the lens?

Q. Match the following columns.
Four combination of two thin lenses are given in List

I

. The radius of curvature of all curved surface is

r

and the refractive index of all the lenses is

1.5

. Match lens combination in List

I

with their focal legth in List

I I

and selected the correct answer using the code given below the lists.

Q. A double convex lens made of glass has both radii of curvature of magnitude 20 cm. Incident light rays parallel to the axis of the lens will converge at a distance at
[Given refractive index of glass = 1.5 ]

What is the relation between refractive indices $μ_{1}, μ_{2} and μ_{3}$ if the behaviour of light rays is as shown in the figure. The refractive index of medium to the left of the lens is $μ_{1}$ , that of lens is $μ_{3}$ and that of medium to the right of lens is $μ_{2}$ .

Join BYJU'S Learning Program