Spherical mirrror 2?

You wish to create an image that is 10 meters from an object. This image is to be inverted and half the height of the object. You wish to accomplish this using one spherical mirror.


Part A


What is the focal length of the mirror that would accomplish this?


Express your answer in meters, as a fraction or to three significant figures.


Part B


Is this a concave or convex mirror?


1.concave


2.convex


Part C


What is the magnitude r of the radius of curvature of this mirror? Express your answer in meters, as a fraction or to three significant figures.


Part D


What type of image is created, real or virtual?


a) real


b)virtual

Spherical mirrror 2?
Part A





As the image is inverted,the image is real and the spherical mirror must be concave.





The magnification 'm' is -0.5 = - v /u





v / u = 0.5 or v = u / 2





thus v and u have same sign, it means





Let object distance 'u' from mirror be 'x' meter





As image distance from the object is 10 meter


then image distance 'v' from the mirror is (10 + x)





But v= u / 2





therefore (10+x ) = (x/2)





x= - 20 m





Object is at 20 m from mirror and image is 10 m from mirror





The mirror formula 1/ f = 1/v + 1/u gives





1/f =1/(-10) + 1 / (-20)





1/f= -3 /20





Focal length of concave mirror is -20 /3 meter = -6.667 meter


______________________________________...


Part B


Only concave mirrors form real inverted image smaller than the object.l








As the image is inverted,the image is real, It is a concave mirror


______________________________________...


Part C


The radius of curvature is twice the focal length.


The radius of curvature is 40 /3=13.333 meter


______________________________________...


Part D





The image is inverted,( only concave mirrors form real inverted image smaller than the object) therefore the image is real
Reply:Ok, let's remember :





1 / p + 1 / q = 1 / f





p = object distance





q = image distance





If the image is 10 meters from the object, then : p - q = 10





" I am considering that the image is in the same side as the object"





also, the image is inverted, and it's half the height of the object, so then :





-q / p = - 1/2





It's minus 1/2, because it's inverted, and half height of the object :





q = p /2





p - q = 10





then : p = 20 and q = 10





Then :





1 / 20 + 1 / 10 = 1 / f





20 / 3 = f





f = 6.223 cm %26gt;%26gt;%26gt;%26gt;%26gt; Focal lenght





The mirror, is a concave mirror





The image is real





Hope that helps

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