A concave mirror produces a real image of 10mm tall of an object 2.5 mm tall placed at a 5 cm from the mirror calculate the focal length of the mirror and the position of the image

Dear Student ,

Given that , hi=10 mm  , and  ,  ho=2.5 mm 
magnification , m= -vu=hiho
where v is the image distance , u is object distance , 

 

-vu = -102.5 ,  vu = 10025  vu = 4 i.e v=4u

 

u = -5cm ,

v= 4(u) so , v = (-5) (4) i.e. -20cm

 

1f = 1v +1u  1f = -120 -15    1f = (-1-4)20  1f = -520  1f = -14 i.e f= -4cm

 here minus sign indicates that the mirror is concave mirror

Regards

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