Question

The thickness of a plano-convex lens is 4 cm. When it is placed on a horizontal table in such a way that its curved surface be in contact with the table, then the depth of a bottom-point of the lens appears 3 cm. If the lens is inverted so that its plane surface be in contact with the table, then the apparent depth of the centre of the lens-surface is found to be (25/8) cm. Determine the focal-length of the lens.     

Solution

Correct option is

75 cm

 

In the first position, the curved surface of the lens is in contact with the table. Let the contact-point O be an object. The light rays starting from O, after refraction in air at the plane surface of the lens, forms virtual image Iof the object O. Now, as given, we have 

                    

Putting these values in the formula for refraction at a surface

     

Here the refracting surface is plane whose radius R = ∞.

                                         

or                           n = 3/4.

Since light-rays are going form glass to air; here n is refractive index of air with respect to glass (n = gna = 3/4).

In the second position, the plane surface of the lens is in contact with the table. Now, the virtual image I of the centre O of the plane surface of the lens is formed due to refraction at the curved surface of the lens. Again, as given

 u = CO = – 4 cm and v = CI = –(25/8) cm and n = 3/4

(calculated above)   

Let R be the radius of the curved surface of the lens.  

Putting the values of uv and n in the formula 

          

                              

or                           

or                                                               

or                           R = –25 cm.

The focal length f of the lens in air is given by

                               

Where n is refractive index of glass of lens with respect to air.

Here 

 

       

or f = 75 cm.   

SIMILAR QUESTIONS

Q1

A 2.0 cm tall object is placed 15 cm from a concave mirror of focal length 10 cm. How far is the image from the mirror? 

Q2

An object 1.0 cm tall is placed 8 cm in front of a concave mirror of radius of curvature 24 cm. What is the size and the nature of the image?

Q3

A concave mirror forms a real image four times the size of the object placed at a distance of 10 cm from it. What is the radius of curvature of the mirror?   

Q4

In Young’s double slit experiment, the 10th maximum of wavelength λ1 is at a distance y1 from its central maximum and the 5th maximum of wavelength λ2 is at a distance y2 from its central maximum. The ratio y1/y2will be   

Q5

White light is used to illuminate the two slits in Young’s double slit experiment. The separation between the slits is d and the distance between the screen and the slit is D (>> d). At a point on the screen directly in front of on the slits, certain wavelengths are missing. The missing wavelengths are (here m = 0, 1, 2, … is an integer)     

Q6

In Young’s double slit experiment using two identical slits, the intensity of the maximum at the centre of the screen is I. What will be the intensity at the centre of the screen if one of the slits is closed?   

Q7

Glycerine (refractive index 1.4) is poured into a large jar of radius 0.2 m to a depth of 0.1 m. There is a small light source at the centre of the bottom of the jar. Find the area of the surface of glycerine through which the light passes.  

Q8

A ray of light travelling in glass (refractive index, ang = 3/2) is incident on a horizontal glass-air surface at the critical angle c. If a thin layer of water (refractive index, anw = 4/3) is now poured on the glass-air surface, at what angle will the ray of light emerge into air at the water-air surface?

Q9

The radius of curvature of the convex surface of a thin plano-convex lens is 20 cm. Refractive index of the medium of the lens is 1.5. Calculate the focal length of the lens.   

Q10

The focal length of a convex lens in air is 20 cm. What will be its focal length if it is immersed in a liquid of refractive index 1.35? Refractive index of glass is 1.50.