Convex lens

The convex lens consists of two spherical segments (dimensions given in mm). Calculate its weight if the density of the glass is 2.5 g/cm3. Dimensions: 60mm in length and width of the upper part 5mm, the width of the lower part 8mm

Correct answer:

m =  1.5275 g

Step-by-step explanation:

ρ=2.5 g/cm3 D=60 mm a=5 mm b=8 mm  v=b−a=8−5=3 mm  V1​=a⋅ D=5⋅ 60=300 mm3  r2 = (D/2)2 + (r−v)2 r2 = (D/2)2 + r2−2⋅ r⋅ v+ v2  0=(D/2)2−2⋅ r⋅ v+v2 0=(60/2)2−2⋅ r⋅ 3+32  12r=1818  r=121818​=151.5  r=2303​=151.5  V2​=61​⋅ π⋅ v⋅ (3⋅ D/2+v2)=61​⋅ 3.1416⋅ 3⋅ (3⋅ 60/2+32)≐155.5088 mm3  V=V1​+2⋅ V2​=300+2⋅ 155.5088≐611.0177 mm3  V3​=V→ cm3=V:1000  cm3=611.0177:1000  cm3=0.61102 cm3  m=ρ⋅ V3​=2.5⋅ 0.611=1.5275 g

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