A 3.0 cm-tall object is 30 cm in front of a converging lens that has a 20 cm foc

Question

A 3.0 cm-tall object is 30 cm in front of a converging lens that has a 20 cm focal length. Please show work

a) Calculate the image position and the image height.

b)Draw a ray-tracing diagram and determine the imaging characteristics for each of the following situations.

i) s = 50 cm

Image size_________

Image type_________

Image location_________

Image orientation_________

ii) s = 40 cm

Image size_________

Image type_________

Image location_________

Image orientation_________

iii) s = 10 cm

Image size_________

Image type_________

Image location_________

Image orientation_________

Explanation / Answer

1/p + 1/q = 1/f

p=object distance = 30 cm
q=image distance
f=focal length = + 20 cm

1/30 + 1/q = 1/20

1/q = 1/20-1/30 = 1/60

q=60 cm, so the image is 60 cm behind the converging lens (the sign convention for converging lenses is that positive image distances are behind the lens; negative object distances are in front of the lens)

the magnification is given by m = q/30 =60/30 = 2

real image

1)

1/p + 1/q = 1/f

p=object distance = 50 cm
q=image distance
f=focal length = + 20 cm

1/50 + 1/q = 1/20

1/q = 1/20-1/50 = 3/100

q=100/3 cm, so the image is 100/3 cm behind the converging lens (the sign convention for converging lenses is that positive image distances are behind the lens; negative object distances are in front of the lens)

the magnification is given by m = q/30 =100/90 = 1.11

real image

2)1/p + 1/q = 1/f

p=object distance = 40 cm
q=image distance
f=focal length = + 20 cm

1/40 + 1/q = 1/20

1/q = 1/20-1/40 = 1/40

q=40 cm, so the image is 40cm behind the converging lens (the sign convention for converging lenses is that positive image distances are behind the lens; negative object distances are in front of the lens)

the magnification is given by m = -q/30 =-40/30 = -1.33

real image

3)1/p + 1/q = 1/f

p=object distance = 10 cm
q=image distance
f=focal length = + 20 cm

1/10 + 1/q = 1/20

1/q = 1/20-1/10 = -1/20

q=-20 cm, so the image is 20 cm ahead the converging lens (the sign convention for converging lenses is that positive image distances are behind the lens; negative object distances are in front of the lens)

the magnification is given by m = q/30 =-20/30 = -0.667

virtual image

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