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Two plano concave lens of glass of refractive index 1.5 have radii of curvature of 20 and 30 cm. They are placed in contact with curved surfaces towards each other and the space between them is filled with a liquid of refractive index (4//3). Find the focal length length of the system.

Answer» <html><body><p></p>Solution :As shown in the <a href="https://interviewquestions.tuteehub.com/tag/figure-987693" style="font-weight:bold;" target="_blank" title="Click to know more about FIGURE">FIGURE</a> the system is equivalent to combination of three <a href="https://interviewquestions.tuteehub.com/tag/thin-707663" style="font-weight:bold;" target="_blank" title="Click to know more about THIN">THIN</a> lenses in <a href="https://interviewquestions.tuteehub.com/tag/contact-25916" style="font-weight:bold;" target="_blank" title="Click to know more about CONTACT">CONTACT</a> i.e., `1/F=1/f_1+1/f_2+1/f_3` <br/> But by <a href="https://interviewquestions.tuteehub.com/tag/lens-1071845" style="font-weight:bold;" target="_blank" title="Click to know more about LENS">LENS</a> maker.s formula <br/> `1/f_1=[3/2-1][1/(-infty)-1/20]=-1/40` <br/> `1/f_2=[4/3-1][1/20+1/30]=5/180` <br/>`1/(f_3)=[3/2-1][1/(-30)-1/(-infty)]=-1/60 so, 1/f=-1/40+5/180-1/60` <br/> `i.e., 1/F=(-90+10-6)/360 or F=-72cm` <br/>i.e., the system will behave as a divergent lens of focal <a href="https://interviewquestions.tuteehub.com/tag/length-1071524" style="font-weight:bold;" target="_blank" title="Click to know more about LENGTH">LENGTH</a> 72cm. <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_DOC_OBJ_PHY_XII_V02_A_C02_SLV_079_S01.png" width="80%"/></body></html>


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