Lens Maker Formula, Silvering Of Lens (JEE LEVEL)

Q.1

A plastic hemisphere has a radius of curvature of 8 cm and an index of refraction of 1.6.  On the axis halfway between the plane surface and the spherical one (4 cm from each) is a small object O.  The distance between the two images when viewed along the axis from the two sides of the hemisphere is approximately

(a)          2.0 cm above P                         

(b)          1.5 cm above P                         

(c)           2.0 cm below P                         

(d)          1 cm above P

Ans (d)

Q.4

Two plano-convex lenses of glass of refractive index 1.5 have radii of curvature 20 cm and 30 cm respectively. They are placed in contact with the curved surfaces towards each other and the space between them is filled with water (m = 4/3). The focal length of the combination is

(a) -60 cm          (b) 72 cm           (c) 70 cm            (d) 60.3 cm

Ans.  (b)

Q.5

A thin convergent glass lens (m_g = 1.5) has a power of +5.0 D. When this lens is immersed in a liquid of refractive index m_l, it acts as a divergent lens of focal length 100 cm. The value of m_l is

(a) 4/3              (b) 5/3            (c) 5/4          (d) 6/5

Ans.  (b)

Q.6

Diameter of the flat surface of a circular plano-convex lens is 6 cm and thickness at the center is 3 mm. The radius of curvature of the curved part is

(a) 15 cm             (b) 20 cm             (c) 30 cm           (d) 10 cm

Ans.   (a)

Q.7

A sphere of radius R made of transparent material of refractive index m works like a thin lens having its optical center coinciding with the center of the sphere. The focal length of this thin lens is

(a) \frac{{\mu R}}{{\left( {\mu -1} \right)}} 

(b) \frac{{\mu R}}{{2\left( {\mu -1} \right)}}         

(c) \frac{{\mu R}}{{\left( {\mu +1} \right)}}

(d) \frac{{\left( {\mu -1} \right)R}}{{\left( {\mu +1} \right)}}

Ans.  (b)

Q.8

Refraction takes place at a convex spherical boundary separating air-glass medium. For the image to be real, the object distance ( \displaystyle {{\mu }_{g}}=3/2). (Object is lying in the glass) 

(a)    should be greater than three times the radius of curvature of the refracting surface

(b)    should be greater than two times the radius of curvature of the refracting surface

(c)     should be greater than the radius of curvature of the refracting surface

(d)    is independent of the radius of curvature of the refracting surface

Ans.  (a)

Q.9

A plano convex lens fits exactly into a plano concave lens.  Their plane surfaces are parallel to each other.  If the lenses are made of different materials of refractive indices \displaystyle {{\mu }_{1}} and \displaystyle {{\mu }_{2}} and R is the radius of curvature of the curved surface of the lenses, then focal length of the combination is

(a)          \displaystyle \frac{R}{{{{\mu }_{1}}-{{\mu }_{2}}}}                     

(b)          \displaystyle \frac{{2R}}{{{{\mu }_{2}}-{{\mu }_{1}}}}                    

(c)          \displaystyle \frac{R}{{2\left( {{{\mu }_{1}}-{{\mu }_{2}}} \right)}}     

(d)          \displaystyle \frac{R}{{2-\left( {{{\mu }_{1}}+{{\mu }_{2}}} \right)}}

Ans.   (a)

Q.10

The x-z plane separates two media A and B of refractive indices \displaystyle {{\mu }_{1}}=1.5\,\,and \displaystyle {{\mu }_{2}}=2\,\,. A ray of light travels from A to B.   Its directions in the two media are given by unit vectors \displaystyle {{\vec{u}}_{1}}\,=\,a\hat{i}\,+\,b\hat{j} and  \displaystyle {{\vec{u}}_{2}}\,=\,c\hat{i}\,+\,d\hat{j}Then 

(a)          \displaystyle \frac{a}{c}=\frac{4}{3}    

(b)          \displaystyle \frac{a}{c}=\frac{3}{4}    

(c)          \displaystyle \frac{b}{d}=\frac{4}{3}   

(d)          \displaystyle \frac{b}{d}=\frac{3}{4}

Ans.  (a)