A light wave (wavelength A) arrives at a point \'A\' where it splits two. One wa

Question

A light wave (wavelength A) arrives at a point 'A' where it splits two. One wave train travels straight to a point 'D' The separation 'A rightarrow D' is 41. The second wave train travels along a jointed path 'A rightarrow B rightarrow C rightarrow D' which is made possible by placing mirrors at the "joints". The middle segment runs parallel to the straight path 'A rightarrow D' and is half its length. 'B rightarrow C' is also '1' units above the straight path 'A rightarrow D'. 'A rightarrow B' and 'C rightarrow D' arc of equal size. Draw the description and be sure to show mirrors. in terms of'1', give the length of the path 'A rightarrow B rightarrow C rightarrow D'. in terms of '1', give the path length diff. between the two paths. Assuming the point 'D' is a point of complete darkness; write down the equation expressing the fact (the appropriate value set for n must be given). if 'A' is 414 nm, determine the min. area enclosed by two paths provided 'D' is a point of complete darkness.

Explanation / Answer

length of the path A -> B -> C -> D      = sqrt[(3l)2 + l2]

                                                               = 3.162 l

path difference between two paths = 4 l   - 3.162 l  

                                                       = 0.838 l

Equation for complete darkness

=>   d * (D/L) = n * lambda

Here, D = 414 * 10-9 * 0.838/4

               =    8.67 * 10-8 m

=> minimum area enclosed = 3.14 * 8.67 * 10-8 * 8.67 * 10-8

                                                               = 2.36 * 10-14 m2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.