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| 1. |
Obtain mirror equation for the real image obtained by concave mirror. |
| Answer» <html><body><p></p>Solution :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XII_P2_C09_E01_012_S01.png" width="80%"/><br/>An object AB is perpendicular to principal axis away from C of a concave mirror.<br/>AM ray from point A incidents on mirror at M and reflected ray passes through principal <a href="https://interviewquestions.tuteehub.com/tag/focus-25840" style="font-weight:bold;" target="_blank" title="Click to know more about FOCUS">FOCUS</a> F.<br/>AP ray from point A incidents on pole P and reflects back in form of PA.<br/>These both reflected rays intersect at A., hence A. is real image of A.<br/>A.B. is image of object AB due to reflection of rays from mirror.<br/>Let FP = focal length f<br/>CP = radius of curvature R<br/>BP = object distance u<br/> B.P= image distance v<br/>For paraxial rays, MP can be considered to be a straight <a href="https://interviewquestions.tuteehub.com/tag/line-1074199" style="font-weight:bold;" target="_blank" title="Click to know more about LINE">LINE</a> perpendicular to CP.<br/>The two right-angled triangles A.B.F and MPF are similar.<br/>`therefore(B.A.)/(PM)=(B.F)/(FP)`<br/>But PM = BA<br/>`therefore (B.A.)/(BA)=(B.F)/(FP)`....(1)<br/>Since `angleAPB = angleA.PB.`, the right angled triangles A.B.P and ABP are also similar. Therefore,<br/>`therefore(B.A.)/(BA)=(B.P)/(BP)`...(2)<br/>Comparing Equations (1) and (2), <br/>`(B.F)/(FP)=(B.P)/(BP)`<br/>but B.F = B.P - FP<br/>`therefore (B.P-FP)/(FP)=(B.P)/(BP)` ....(3)<br/>Now, <a href="https://interviewquestions.tuteehub.com/tag/according-366619" style="font-weight:bold;" target="_blank" title="Click to know more about ACCORDING">ACCORDING</a> to sign <a href="https://interviewquestions.tuteehub.com/tag/convention-933064" style="font-weight:bold;" target="_blank" title="Click to know more about CONVENTION">CONVENTION</a>, B.P = - v, FP = - f, BP = - u<br/>From equation (3),<br/>`(-v+f)/(-f)=(-v)/(-u)`<br/> `therefore (v-f)/(f)=v/u` <br/> `therefore v/f-1=v/u`<br/>`therefore v/f=1+v/u`<br/>Now,dividing by v,<br/>`therefore 1/f=1/v+1/u`<br/>Which is mirror equation and it is called Gaussian equation as it was given by scientist Gauss.</body></html> | |