RAY OPTICS AND OPTICAL INSTRUMENTS QUIZ 19

 

Ray Optics and Optical Instruments Quiz-19

Dear Readers,

As per analysis for previous years, it has been observed that students preparing for NEET find Physics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Biology due to their medical background. Furthermore, sections such as Physics are dominantly based on theories, laws, numerical in comparison to a section of Biology which is more of fact-based, life sciences, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced. .

Q1.  Venus looks brighter than other stars because

•   It has higher density than other stars
•   It is closer to the earth than other stars
•   It has no atmosphere
•   Atomic fission takes place on its surface

Solution
𝐼 ∝ 1/𝑟²

Q2. A ray of light travelling in water is incident on its surface open to air. The angle of incidence isθ, which is less than the critical angle. Then there will be

•   Only a reflected ray and no reflected ray
•   Only a reflected ray and no reflected ray
•   A reflected ray and a refracted ray and the angle between then would be less than 108° − 2θ
•   A reflected ray and a refracted ray and the angle between then would be greater than 108° − 2θ

Solution
Since θ < θc, both reflection and refraction will take place. From the figure we can see that angle between reflected and refracted rays 𝛼is less than 180° − 2θ.

Q3.   If the focal length of objective and eye lens are 1.2 𝑐𝑚 and 3 𝑐𝑚 respectively and the object is put 1.25 𝑐𝑚 away from the objective lens and the final image is formed at infinity. The magnifying power of the microscope is

•   150
•   200
•   250
•   400

Solution
𝑚∞ = − 𝑣_o/𝑢₀ × 𝐷/𝑓_e From 1/𝑓_o = 1/𝑣_o − 1/𝑢_o ⇒ 1/(+1.2) = 1/𝑣_o − 1/(−1.25) ⇒ 𝑣_o = 30 𝑐𝑚 ∴ |𝑚_∞| = 30/1.25 × 25/3 = 200

Q4.  The refractive index of a piece of transparent quartz is the greatest for

•   Red light
•   Violet light
•   Green light
•   Yellow light

Solution
𝜇 ∝ 1/𝜆 ,𝜆𝑟 > 𝜆𝑣

Q5. Refractive index for a material for infrared light is

  Equal to that of ultraviolet light

  Less than for ultraviolet light

  Equal to that for red colour of light

  Greater than that for ultraviolet light

Solution
  𝜇 ∝ 1/𝜆 .

Q6.  In vacuum the speed of light depends upon

•   Frequency
•   Wave length
• Velocity of the source of light
•   None of these

Solution
In vacuum speed of light is constant and is equal to 3 × 10𝑚/𝑠

Q7. A point source of light moves in a straight line parallel to a plane table. Consider a small portion of the table directly below the line of movement of the source. The illuminance at this portion varies with this distance 𝑟 from the source as

•   ∝ 1/𝑟
•   ∝ 1/𝑟²
•   ∝ 1/𝑟³
•   ∝1/𝑟³

Solution

𝐸 = 𝐼 cosθ/𝑟2 ⇒ 𝐸 = 𝐼ℎ/𝑟³

 

  Or 𝐸 ∝ 1/𝑟³

Q8. When a plane mirror is placed horizontally on a level ground at a distance of 60𝑚 from the foot of a tower, the top of the tower and its image in the mirror subtend an angle of 90° at the 𝑒𝑦𝑒. The height of the tower will be

•   30𝑚
•   60𝑚
•   90𝑚
•   120𝑚

Solution
tan45° = ℎ/60 ⇒ ℎ = 60 𝑚

Q9. The distance 𝜈 of the real image formed by a convex lens is measured for various object distance 𝑢 . A graph is plotted between 𝜈 and 𝑢 . Which one of the following graphs is correct?

•  
  
  
  
•  
  
  
  
•   
  
  
  
•   
  
  
  

Solution
Think in terms of rectangular hyperbola

Q10.  A plano-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 from 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?

•   20cm
•   30cm
•   60cm
•   80cm

Solution
A plano-convex lens behaves as a concave mirror if it’s one surface (curved) is silvered. The rays refracted from plane surface are reflected from curved surface and again refract from plane surface. Therefore, in this lens two refractions and one reflection occur. Let the focal length of silvered lens is 𝐹. /𝐹 = 1/𝑓 + 1/𝑓 + 1/𝑓_m = 2/𝑓 + 1/𝑓_m Where 𝑓 = focal length of lens before silvering 𝑓_m =focal length of spherical mirror.

∴ 1/𝐹 = 2/𝑓 + 2/𝑅 …..(𝑖) 

(∵ 𝑅 = 2𝑓_m 𝑛𝑜𝑤 , 1 𝑓 = (𝜇 − 1)(1 𝑅₁ - 1 𝑅₂ ) ….(𝑖𝑖) 

 ℎ𝑒𝑟𝑒, 𝑅₁ = ∞,𝑅₂ = 30 𝑐𝑚 ∴ 1/𝑓 = (1.5 − 1)(1/∞−1/30) ⟹ 1/𝑓= − 0.5/30= −1/60 ⟹ 𝑓 = −60 𝑐𝑚

 Hence from eq (i) 1/𝐹 = 2/60 + 2/30 = 6/60 𝐹 = 10 𝑐𝑚

 Again given that, Size of object = size of image ⟹ 𝑂 = 𝐼 ∴ 𝑚 = −𝑣/𝑢 = 𝐼/𝑂 ⟹ 𝑣/𝑢 = −1 ⟹ 𝑣 = −𝑢 Thus, from lens formula 1/𝐹 = 1/𝑣 − 1/𝑢 1/10 = 1/−𝑢 − 1/𝑢 1/10

 = − 2/𝑢 ∴ 𝑢 = −20 𝑐𝑚 

Hence, to get a real image, object must be placed at a distance 20 cm on the left side of lens