question_answer 14)

Use the mirror equation to deduce that (a) an object placed between f and 2f ofa concavemirror produces a real image beyond 2f. (b)a convex mirror always produces a virtualimage independent of the location of the object. (c) the virtual image produced by a convex mirror is always diminished in size and islocated between the focus and the pole. (d)an object placed between the pole and focusof a concave mirror produces a virtual andenlarged image.  

Answer:

(a) For a concave mirror, the mirror formula        is given by          ?(i) where both/and u are negative i.e. and u < 0 Then, for an object between f and 2f, wehave or Multiplying by -1, the inequality becomes Using equation (i), we have It means that if v is negative, the imageformed is real and beyond 2f. (b) For a convex mirror, using the mirror formulawhere f> 0 and u < 0 we findthat v is always positive i.e. the image lies on the right of the mirror and is thus a virtualimage. (c) The magnification of mirror, For a convex mirror f is positive whereas u isnegative. Therefore f- u is always greater than f  i.e. i.e., the imageis diminished (d) For a concave mirror, f< 0, u < 0u<0 For an object placed in between pole andprincipal focus, But using mirror formula, , wefind, i.e. v is positive and lies to theright of pole. the image is virtual. Also, magnification, Since i.e., m is positive and greater than 1. So, theimage is enlarged.