Question

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     

Solution

Correct option is

Convex, 6 cm

 

or                 v = – 3 u

Now             u = –10 cm, therefore v = +30 cm.    

If F is the focal length of the combination, we have  

                       

  

Focal length of the concave lens B = f1 = –30cm. If f2 is the focal length of lens A, we have

                      

Which gives        f2 = 6 cm.

Since f2 is positive, the lens is convex.

SIMILAR QUESTIONS

Q1

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).      

Q2

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     

Q3

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  

Q4

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

Q5

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? 

Q6

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      

Q7

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   

Q8

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? 

Q9

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? 

Q10

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?