A thin lens projects an image at a distance q = -15 cm when anobject is placed p

Question

A thin lens projects an image at a distance q = -15 cm when anobject is placed p = 5 cm from it.
a) find the focal length of the lens. b) find the magnification of the image. c) state if the lens is converging or diverging d) construct a ray tracing diagram for this situation andlabel the object, image, and focal point locations p, q, and f,respectively.
the diagram does not need to be a scale.
e) for what object distances (if any) will the image distancebe positive?

a) find the focal length of the lens. b) find the magnification of the image. c) state if the lens is converging or diverging d) construct a ray tracing diagram for this situation andlabel the object, image, and focal point locations p, q, and f,respectively.
the diagram does not need to be a scale.
e) for what object distances (if any) will the image distancebe positive?

Explanation / Answer

Given
The distance between image and lens   Q = -15cm The distance between objectand the lens P = 5cm a ) The thin lens equation                 ( 1 / P ) + ( 1 / Q ) = -( 1 / f )                   (1 / 5 ) + ( 1 / -15 )   = 1 / f                                focal length of the lens f = - 7.49 cm b) magnificationof the image                   M =   - Q / P                           = - ( -15 / 5 )                         = 3 c ) The lens is a diverging lens         since focal lengthof the lens is negative . e)     let the image distance distancebe +15 cm              focal length of the   lens is - 7.49 cm         so object distance     1 / P = (1 / f ) - ( 1 / Q )                                       = ( - 1 / 7.49 ) - ( 1 / 15                                       = -4.99 cm           soodject distance   P = - P         so the objectbe placed right side of the lens in 4.99 cm

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