Two identical glass $\left({\mu }_g=3/2\right)$ equi-convex lenses of focal length $f$ each are kept in contact. The space between the two lenses is filled with water $\left({\mu }_w=4/3\right)$. The focal length of the combination is

(a)  $f/3$             (b) $f$

(c) $\frac{4f}{3}$               (d) $\frac{3f}{4}$

A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use will be:

An astronomical telescope has an objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance of :
(1) 46.0 cm

(2) 50.0 cm  

(3) 54.0 cm

(4) 37.3 cm 

Match the corresponding entries of Column 1 with Column 2. [Where m is the magnification produced by the mirror]

Column 1                         Column 2 
A. m=-2                     a. Convex mirror   
B. m=-1/2                  b. Concave mirror
C. m=+2                    c. Real image
D. m=+1/2                 d. Virtual Image

(1)A->a and c;B->a and d; C->a and b; D->c and d
(2)A->a and d; B->b and c; C->b and d; D-> b and c
(3)A->c and d; B->b and d;C->b and c;D->a and d
(4)A->b and c; B->b and c; C->b and d; D->a and d

The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of deviation and refracting index of the material of the prism respectively are

(a)30°,$\sqrt{2}$

(b)45°,$\sqrt{2}$

(c)30°,$\frac{1}{\sqrt{2}}$

(d)45°,$\frac{1}{\sqrt{2}}$

$The refracting angle of a prism is A, and refractive index of the material of the prism is cot (A/2).$
$The angle of minimum deviation is-$
$\left(a\right) 180°-3A$
$\left(b\right) 180°-2A$
$\left(c\right) 90°-A$
$\left(d\right) 180°+2A$

A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47, respectively.


The prism will

(1) separate the blue colour part from the red and green colours

(2) separate all the three colours from one another

(3) not separate the three colours at all

(4) separate the red colour part from the green and blue colours

The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ of the prism is

(1)2sinA

(2)2cosA

(3)1/2cosA

(4)tanA

A plane-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices in  μ₁ and μ₂ and R is the radius of curvature of the curved surface of the lenses. then the focal length of the combination is

(1) R/2(μ₁₊μ₂₎

(2) R/2(μ_1-μ₂₎

(3) R/(μ_1-μ₂₎

(4) 2R/(μ2-μ₁₎