Answer to Question #277467 in Optics for jack02

Question

A 2 cm tall object is placed 3 cm from a concave mirror. The focal length is 5 cm.

Include units in your answers as you fill in the table.

Show your calculation of the image location.

Show your calculation of the image height.

Show your complete graphical solution to this problem.

Answer 1

${According\,to\,new\,cartesian\,sign\,convention}\\ {Object\,distance,\,u=-3cm}\\ {Focal\,length\,of\,concave\,mirror\,f=-5cm}\\ {Height\,of\,the\,object\,h_o=2cm}\\ {according\,to\,mirror\,formula;\,\frac{1}{v}+\frac{1}{u}=\frac{1}{f}}\\ {\frac{1}{v}=\frac{1}{f}-\frac{1}{u}}\\ {\frac{1}{v}=\frac{1}{-5}-\frac{1}{-3}}\\ {v=7.5cm}\\ {The\,image\,ia\,formed\,at\,distance\,of\,7.5cm\,from\,the\,mirror\,on\,the\,opposite\,side\,of\,the\,iobject}\\ {magnification\,m=\frac{-v}{u}=\frac{h_i}{h_o}}\\ {\frac{-7.5}{-3}=\frac{h_i}{2}=h_i=5cm}\\ {positive\,sign\,shows\,that\,the\,image\,is\,upright}\\$