question_answer

An equiconvex lens of focal length 10 cm (in air) and R. I. 3/2 is put at a small opening on a tube of length 1m fully filled with liquid of R. 1.4/3. A concave mirror of radius of curvature 20 cm is cut into two halves \[{{M}_{1}}\,and\,{{M}_{\text{2}}}\] and placed at the end of the tube. \[{{M}_{1}}\,and\,{{M}_{\text{2}}}\] are placed such that their principal axes AB and CD respectively are separated by 1mm each from the principal axis of the lens. A slit S placed in air illuminates the lens with light of frequency\[7.5 \times  1{{0}^{14}}Hz\]. The light reflected from \[{{M}_{1}}\,and\,{{M}_{2}}\] forms interference pattern on the left end EF of the tube. O is an opaque substance to cover the hole left by\[{{M}_{1}}\,\,and\,\,{{M}_{2}}\]. Width of the fringes on EF is\[\left( x \times  10 \right)\mu m\]. Find the value of x in metre.

Answer:

(6)