Please wait...
Contact Us
Contact
Need assistance? Contact us on below numbers

For Study plan details

10:00 AM to 7:00 PM IST all days.

For Franchisee Enquiry

OR

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this number

93219 24448 / 99871 78554

Mon to Sat - 10 AM to 7 PM

Find the value of  m

qsnImg
Asked by venkat 1st March 2018, 12:51 PM
Answered by Expert
Answer:
as illustrated in the diagram, light rays originating from point source upto critical angle are refracted and above critical angle total internal reflection takes place. Hence the refracted rays will be seen as circular spot, when viewed from top.
 
Using spherical coordinates, the area of the spot is given by

begin mathsize 12px style integral subscript 0 superscript theta subscript C end superscript R squared cos theta space d theta space d phi space equals space 2 pi R squared space integral subscript 0 superscript theta subscript C end superscript cos theta space d theta space equals space 2 pi R squared sin space theta subscript C space b u t space sin space theta subscript C space equals 1 over mu h e n c e space a r e a space equals space fraction numerator 2 pi R squared over denominator mu end fraction space equals space 2 pi cross times 5 square root of 5 cross times 5 square root of 5 cross times 2 over 3 space equals space fraction numerator 500 pi over denominator 3 end fraction space s q. c m end style
 
as per the question, m = ( 250π)/3 sq.cm
Answered by Expert 1st March 2018, 2:37 PM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!

Free related questions

13th May 2023, 10:08 PM
8th March 2024, 5:01 PM

Chat with us on WhatsApp