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 Multiple Choice QuestionsMultiple Choice Questions

1.

A car is fitted with a convex sideñview mirror of focal length 20 cm.Asecond car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is

  • 1/15 m/s

  • 10 m/s

  • 15 m/s

  • 1/10 m/s


A.

1/15 m/s


The mirror formula

1 over straight u space plus 1 over straight v space equals space 1 over straight f
1 over straight v space plus space fraction numerator 1 over denominator negative 280 end fraction space equals space 1 over 20
1 over straight v space space equals space 1 over 20 plus 1 over 280
1 over straight v space plus fraction numerator 14 plus 1 over denominator 280 end fraction
straight v space equals space 280 over 15
straight v subscript 1 space equals space minus space open parentheses straight v over straight u close parentheses squared. straight v
therefore space straight v subscript 1 space equals space minus open parentheses fraction numerator 280 over denominator 15 space straight x space 280 end fraction close parentheses squared.15 space
therefore space equals space straight v subscript 1 space equals space fraction numerator negative 15 over denominator 15 space straight x space 15 end fraction
straight v subscript 1 space equals space minus 1 over 15 space straight m divided by straight s
175 Views

2.

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 45o with the x-axis meets the experimental curve at P. The coordinates of P will be

  • (2f, 2f)

  • (f/2, f/2)

  • (f,f)

  • (4f, 4f)


A.

(2f, 2f)

It is possible when object kept at centre of curvature.
u = v
u = 2f,
v = 2f.

476 Views

3.

The diameter of the plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is 2 × 108 m/s, the focal length of the lens is 

  • 15 cm

  • 20 cm

  • 30 cm

  • 10 cm


C.

30 cm



straight R squared space equals straight d squared space plus space left parenthesis straight R minus straight t right parenthesis squared
straight R squared minus straight d squared space equals space straight R squared space open curly brackets 1 minus straight t over straight R close curly brackets squared
1 minus straight d squared over straight R squared space equals space 1 minus fraction numerator 2 straight t over denominator straight R end fraction
straight R space equals space fraction numerator left parenthesis 3 right parenthesis squared over denominator 2 space straight x left parenthesis 0.3 right parenthesis end fraction space equals space 90 over 6 space equals space 15 space cm
1 over straight f space equals space left parenthesis straight mu minus 1 right parenthesis space open parentheses 1 over straight R subscript 1 minus 1 over straight R subscript 2 close parentheses
1 over straight f space equals space open parentheses 3 over 2 minus 1 close parentheses open parentheses 1 over 15 close parentheses
straight f equals space 30 space cm
366 Views

4.

The angle of incidence at which reflected light totally polarized for reflection from air to glass (refractive index n), is

  • sin−1 (n

  • sin−1 (1/n)

  • tan−1 (1/n)

  • tan−1 (n)


D.

tan−1 (n)

Brewster’s law: According to this law the ordinary light is completely polarised in the plane of incidence when it gets reflected from transparent medium at a particular angle known as the angle of polarisation. n = tan ip.

286 Views

5.

Two lenses of power -15D and +5D are in contact with each other. The focal length of the combination is

  • -20 cm

  • -10 cm

  • +20 cm

  • +10 cm


B.

-10 cm

P = P1 + P2 = −10
f= 1/P
 = 0.1 m 
 = -10 cm

564 Views

6.

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by 

  • a vernier scale provided on the microscope

  • a standard laboratory scale 

  • a meter scale provided on the microscope 

  • a screw gauage provided on the microscope


A.

a vernier scale provided on the microscope

206 Views

7.

A plane convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object?

  • 20 cm

  • 30 cm

  • 60 cm

  • 80 cm


A.

20 cm

1 over straight F space equals space 2 over straight f subscript 1 space plus 1 over straight f subscript straight m
and space 1 over straight f subscript 1 space equals space left parenthesis 1.5 minus 1 right parenthesis space open parentheses 1 over infinity minus fraction numerator 1 over denominator negative 30 end fraction close parentheses space equals space 1 over 60
and space straight f subscript straight m space equals space 15 space cm
therefore comma space straight F space equals space 10 space cm
object space should space be space placed space at space 20 space cm space from space the space lens.
921 Views

8.

An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film? 

  • 7.2 m

  • 2.4 m

  • 3.2 m

  • 5.6 m


D.

5.6 m

Case I: u = –240cm, v = 12, by Lens formula

1 over straight f space equals space 7 over 80
Case space II colon space 12 minus 1 third space equals space 35 over 3 space open parentheses normal space shift space equals space 1 minus 2 over 3 space equals space 1 third close parentheses
straight f equals space 7 over 80
straight u space equals space 5.6

522 Views

9.

Let the xz-plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a refractive index of √2 and medium 2 with z<0 has a refractive index of √3. A ray of light in medium 1 given by the vectorstraight A space equals space 6 square root of 3 space bold i with bold hat on top bold space bold plus bold space 8 square root of 3 space bold j with bold hat on top minus 10 bold k with hat on top is incident on the plane of separation. The angle of refraction in medium 2 is

  • 45° 

  • 60° 

  • 75° 

  • 30° 


A.

45° 

As a refractive index for z>0 and z≤0 is different xy-plane should be the boundary between two media.
Angle of incidence,
space cos space straight i space space equals space open vertical bar fraction numerator straight A subscript straight z over denominator square root of straight A subscript straight x superscript 2 space plus straight A subscript straight y superscript 2 plus straight A subscript straight z superscript 2 end root end fraction close vertical bar space equals 1 half
straight i space equals space 60 to the power of straight o
From space Snell apostrophe straight s space law comma space fraction numerator sin space straight i over denominator sin space straight r end fraction space equals space straight mu subscript 2 over straight u subscript 1 space equals space fraction numerator square root of 3 over denominator square root of 2 end fraction
sin space straight r space equals space fraction numerator square root of 3 space end root space straight x space square root of 2 over denominator square root of 3 space straight x 2 end root end fraction rightwards double arrow space straight r space space equals space 45 to the power of straight o

621 Views

10.

A student measures the focal length of the convex lens by putting an object pin at a distance ‘u’ from the lens and measuring the distance ‘v’ of the image pin. The graph between ‘u’ and ‘v’ plotted by the student should look like


C.

1 over straight v minus 1 over straight u space equals space 1 over straight f
355 Views