Ray Optics and Optical Instruments-Quiz-7

RAY OPTICS AND OPTICAL INSTRUMENTS - 7

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Q1. Choose the correct mirror image of figure given below

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Solution

Q2.An equiconvex lens is cut into two halves along (i) XOX^' and (ii) YOY^'' as shown in figure. Let f,f^',f^'' be the focal length of the lens, of each half in case (i), and of each half in case (ii), respectively

•  f^'=f,f^''=2f
•  f^'=2f,f^''=f
•  f^'=f,f^''=f
•  f^'=2f^',f^''=2f

Solution

In the first case, neither the radii of curvature nor the material of the lens is affected. In the second case, 1/f^'' =(μ-1)(1/R) or
1/f^'' =1/2 (μ-1)(2/R)=1/2f
or f^''=2f

Q3.  A focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25cm in front of it to 50cm, the magnification of its image changes from m_25 to m_50.The ration m_25/m_50 is

•   6°
•  7
•  8
•  9

Solution
1/v-1/u=1/f Or u/v-1=u/f
Or u/v=((u+f)/f)
m=v/u=(f/(u+f))
m_25/m_50 =((20/(-25 + 20)))/((20/(-50 + 20)) )=6

Q4. An object is put at a distance of 5 cm from the first focus of a convex lens of focal length 10 cm.
If a real image is formed, its distance from the lens will be

•  μ>Clockwise, 1.57 cms^(-1)
•  Clockwise, 3.14 cms^(-1)
•  μ>Anticlockwise, 1.57 cms^(-1)
•  Anticlockwise, 3.14 cms^(-1)

Solution

Q5. A light beam is travelling from Region I to Region IV (refer figure). The refractive index in Region I, II, III and IV are n_0,n_0/2,n_0/6 and n_0/8, respectively. The angle of incidence θ for which the beam just misses entering Region IV is

•  sin^(-1)⁡(3/4)
•  sin^(-1)⁡(1/8)
•  sin^(-1)⁡(1/4)
•  sin^(-1)⁡(1/3)

Solution

Q6. Focal length of a thin convex lens is 30 cm. At a distance of 10 cm from the lens, there is a plane refracting surface of refractive index 3/2. Where will the parallel rays incident on the lens converge?

•  At a distance of 27.5 cm from the lens
•  At a distance of 25 cm from the lens
• At a distance of 45 cm from the lens
•  At a distance of 40 cm from the lens

Solution

Q7.A convex lens of focal length 10 cm is painted black at the middle portion as shown in figure. An object is placed at a distance of 20 cm from the lens

•  Only one image will be formed by the lens
•  The distance between the two images formed by such a lens is 6 mm
•  The distance between the images is 4 mm
•  The distance between the images is 2 mm

Solution
Only one image will be formed by this lens system because optic axis of both the parts coincide. Two images would have formed if their optic axis were different

Q8.A gun of mass m_1 fires a bullet of mass m_2 with horizontal speed v_0. The gun is fitted with a concave mirror of focal length f facing toward a receding bullet. Find the speed of separation of the bullet and the image just after the gun was fired

•  (1+m_2/m_1 ) v_0
•  T2(1-m_2/m_1 ) v_0
•  2(1+(2m_2)/m_1 ) v_0
•  2(1+m_2/m_1 ) v_0

Solution

Q9.A rod made of glass, refractive index 1.5 and of square cross section, is bent into the shape shown in figure. A parallel beam of light falls normally on the plane flat surface A. Referring to the diagram, d is the width of a side and R is the radius of inner semicircle. Find the maximum value of ratio d/R so that all light entering the glass through surface A emerges from the glass through surface B

•  1/2
•  1/5
•  1/4
•  2/3

Solution

Q10. An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?

•  25 cm
•  7 cm
•  18 cm
• 27 cm

Solution