Question

A plano-convex lens acts like a concave mirror of 28 cm focal length when its plane surface is silvered and like a concave mirror of 10 cm focal length when its curved surface is silvered. What is the refractive index of the material of the lens?  

Solution

Correct option is

1.55

 

In the first case we have               (∵ fm = ∞) 

                   

In the second case we have

                   

Where fm is the focal length of the curved silvered surface. Hence fm = R/2 where R is the radius of curvature of the curved surface.

Subtracting (i) and (ii) we get

                    

  

From (i) we have f1 = 28 × 2 = 56 cm. Now   

            

  

.

SIMILAR QUESTIONS

Q1

A vessel of depth t is half filled with oil of refractive index  and the other half is filled with water of refractive index . The apparent depth of the vessel when viewed from above is     

Q2

A ray of light, travelling in a medium of refractive index μ, is incident at an angle i on a composite transparent plate consisting of three plates of refractive indices . The ray emerges from the composite plate into a medium of refractive index , at angle x. Then  

Q3

A tank contains a slab of glass 8 cm thick and of refractive index 1.6. Above this is a depth of 4.5 cm of an oil and upon this floats a layer of water 6 cm thick and of refractive index 4/3. To an observer looking down from above, a mark at the bottom of the glass slab appears to be raised up to position 6 cm from the bottom of the slab. The refractive index of oil is

Q4

The principle section of a glass prism is an isosceles triangle ABC with ABAC. The face AC is silvered. A ray incident normally on face AB, after two reflections, emerges from the base BC in a direction perpendicular to it. What is the BAC of the prism? 

Q5

A mark is made on the surface of a glass sphere of diameter 10 cm and refractive index 1.5. It is viewed through the glass from a portion directly opposite. The distance of the image of the mark from the centre of the sphere will be      

Q6

An object and a screen are mounted on an optical bench and a converging lens is placed between them so that a sharp image is received on the screen. The linear magnification of the image is 2.5. The lens is now moved 30 cm nearer the screen and a sharp image is again formed on the screen. The focal length of the lens is   

Q7

A lamp and a screen are set up 100 cm apart and a convex lens is placed between them. The two positions of the lens forming real images on the screen are 40 cm apart. What is the focal length of the lens? 

Q8

A convex lens forms a real image of an object on a screen; the magnification of the image being 3/2. The object and the screen are kept fixed and the lens is moved through a distance of 16 cm when a sharp image is again formed on the screen; the magnification now being 2/3. What is the focal length of the lens? 

Q9

An object is placed at a distance of 10 cm from a co-axial combination of two lenses A and B. The combination forms a real image three times the size of the object. If lens B is concave with a focal length of 30 cm, what is the nature and focal length of lens A     

Q10

A pin is placed 10 cm in front of a convex lens of focal length 20 cm and refractive index 1.5. The surface of the lens farther away from the pin is silvered and has a radius of curvature of 22 cm. How far from the lens is the final image formed?