Question

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   

Solution

Correct option is

14.3 cm

 

If O and I are the object and the screen respectively and L1 and L2 are the two conjugate positions of the lens (fig.), then   

                                     

For lens at L1 we have u = –x and v = 30 + x   

Linear magnification    

        

or                          = 20 cm 

Hence u = –20 cm and v = 30 + 20 = 50 cm.  

   

                            

Which gives                  f = 14.3 cm

SIMILAR QUESTIONS

Q1

A glass prism ABC of refractive index 1.5 is immersed in water of refractive index 4/3 as shown in fig. A ray of light incident normally on face AB is totally reflected at face AC if  

                                                               

Q2

What is the relation between refractive indices μμ1 and μ2 if the behavior of light rays is as shown in fig.

                                                             

Q3

A lens forms a sharp image on a screen. On inserting a parallel sided glass slab between the lens and the screen, it is found necessary to move the screen a distance d away from the lens is order to focus the image sharply. If the refractive index of glass relative to air is μ, the thickness of the glass slab is given by

Q4

A convex lens is placed between an object and a screen which are a fixed distance apart. For one position of the lens the magnification of the image obtained on the screen is m1. When the lens is moved by a distance d, the magnification of the image obtained on the same screen is m2. The focal length of the lens is (m1 > m2).      

Q5

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     

Q6

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  

Q7

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

Q8

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? 

Q9

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      

Q10

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?