4) A concave mirror has a radius of curvature of 74.0 cm. Calculate the image po

Question

4) A concave mirror has a radius of curvature of 74.0 cm. Calculate the image position, magnification,and other characteristics, for an object placed in front of themirror at the positions tabulated below.

object image position (cm) position (cm) magnification Is it real? Is it upright? Is it enlarged? 77.0 Y or N?yesno Y or N?yesno Y or N?yesno 17.0 Y or N?yesno Y or N?yesno Y or N?yesno
Draw ray diagrams to obtain the image characteristics in each case. object image position (cm) position (cm) magnification Is it real? Is it upright? Is it enlarged? 77.0 Y or N?yesno Y or N?yesno Y or N?yesno 17.0 Y or N?yesno Y or N?yesno Y or N?yesno

Explanation / Answer

Given Radius of curvature of concve mirror R = 74cm = 0.74 m a) object distance    P =   77 cm   = 0.77 cm        Spherical mirror equationis               1 / P + 1 / Q = 2 / R                  1 /Q   = 2 / R - 1  /P                            = 2 / 0.74   - 1 / 0.77       imagedistance   Q                      = 0.712 m = 71.2 cm image is formed right side of the lens So the image is real       Magnification   M = -Q / P   = 71.2   / 77 =-0.9246    image is inverted b) object dtstance   P = 17 cm Spherical mirror equation is               1 / P + 1 / Q = 2 / R                  1 /Q   = 2 / R - 1  /P                            = 2 / 0.74   - 1 / 0.17       imagedistance   Q                      = -3.1796 m = -317.96 cm image is formed same side of the object So the image is virtual     Magnification   M = -Q / P   =  -(-317.96 ) / 77 =4.129    image is uprighted             1 / P + 1 / Q = 2 / R                  1 /Q   = 2 / R - 1  /P                            = 2 / 0.74   - 1 / 0.17       imagedistance   Q                      = -3.1796 m = -317.96 cm image is formed same side of the object So the image is virtual     Magnification   M = -Q / P   =  -(-317.96 ) / 77 =4.129    image is uprighted

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