26. The focal length of converging lens is measured for violet, green and red colours. It is respectively f_v, f_g , f_r. We will get​​
    

1. 1. f_v = f_g

   
   
   

   2. f_g > f_r

   
   
   

   3. f_v < f_r

   
   
   

   4. f_v > f_r

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to Cauchy relation
   

   μ = A +	B	+	C	....    Hence f ∝ λ
   	λ2		λ4

   
   ∴ Red light has wavelength greater than violet light. Therefore focal length of lens for red is greater than for violet. (f_r > f_v)

   Correct Option: C

   According to Cauchy relation
   

   μ = A +	B	+	C	....    Hence f ∝ λ
   	λ2		λ4

   
   ∴ Red light has wavelength greater than violet light. Therefore focal length of lens for red is greater than for violet. (f_r > f_v)

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27. Rainbow is formed due to a combination of
    

1. 1. dispersion and total internal reflection ​

   
   
   

   2. refraction and absorption

   
   
   

   3. dispersion and focussing

   
   
   

   4. refraction and scattering

   
   
   

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1. View Hint View Answer Discuss in Forum

   Rainbow is formed due to combination of total internal reflection and dispersion.

   Correct Option: A

   Rainbow is formed due to combination of total internal reflection and dispersion.

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28. 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. 1. 2 sin A

   
   
   

   2. 2 cos A

   
   
   

   3. 	1	cos A
      	2

      
      

   
   
   

   4. tan A

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   According to Snell’s law µ =	sin i
   	sin r

   
   ⇒ (1) sin 2A = (µ) sin A ⇒ µ = 2 cos A

   Correct Option: B

   
   

   According to Snell’s law µ =	sin i
   	sin r

   
   ⇒ (1) sin 2A = (µ) sin A ⇒ µ = 2 cos A

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29. 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. 1. separate all the three colours from one another

   
   
   

   2. not separate the three colours at all

   
   
   

   3. separate the red colour part from the green and blue colours ​

   
   
   

   4. separate the blue colour part from the red and green colours

   
   
   

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1. View Hint View Answer Discuss in Forum

   For total internal reflection, incident angle (i) > critical angle (i_c)
   
   So, sin i > sin i_c
   

   ​sin 45° >	1	⇒ μ > √2 ⇒ 1.414
   	μ

   
   Since refractive index µ of green and voilet are greater than 1.414 so they will total internal reflected. But red colour will be refracted.
   

   Correct Option: C

   For total internal reflection, incident angle (i) > critical angle (i_c)
   
   So, sin i > sin i_c
   

   ​sin 45° >	1	⇒ μ > √2 ⇒ 1.414
   	μ

   
   Since refractive index µ of green and voilet are greater than 1.414 so they will total internal reflected. But red colour will be refracted.
   

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30. 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 minimum deviation and refractive index of the material of the prism respectively, are :​​

1. 1. 45° ,	1
      	√2

   
   
   

   2. 30° , √2

   
   
   

   3. 45° , √2

   
   
   

   4. 30° ,	1
      	√2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given: Angle of incidence ​i = 45°
   angle of prism, ​A = 60°; ​
   Angle of minimum deviation, ​δ_m = 2i – A = 30°
   ​Refractive index of material of prism.
   

   μ =	sin		A + δm
   			2
   			sin A / 2

   
   

   =	sin 45°	=	1	.	2	= √2
   	sin 30°		√2		1

   Correct Option: B

   Given: Angle of incidence ​i = 45°
   angle of prism, ​A = 60°; ​
   Angle of minimum deviation, ​δ_m = 2i – A = 30°
   ​Refractive index of material of prism.
   

   μ =	sin		A + δm
   			2
   			sin A / 2

   
   

   =	sin 45°	=	1	.	2	= √2
   	sin 30°		√2		1

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