The characteristics that follow are characteristics of two of Galileo's surviving double-convex lenses. The numbers given are magnitudes only; you must supply the correct signs. L 1: front radius 950 mm, rear radius 2700 mm, refractive index 1.528; L2: front radius 535 mm, rear radius 50,500 mm, refractive index 1.550. a. What is the largest angular magnification that Galileo could have obtained with these two lenses? b. How long would this telescope be between the two lenses?

L 1: front radius 950 mm, rear radius 2700 mm, refractive index 1.528;

We shall use lens maker's formula, that is

1/f = (μ-1) (1/R₁ - 1/R₂), μ is refractive index of the lens, R₁ and R₂ are radius of curvature of front and rear curved surface.

1/f₁ = (1.528-1) (1/950 + 1/2700)

f₁ = 1331 mm

L2: front radius 535 mm, rear radius 500 mm, refractive index 1.550.

1/f₂ = (1.550-1) (1/535 + 1/500)

f₂ = 470 mm

largest angular magnification possible

= f₁ / f₂

= 1331 / 470

= 2.83 (approx)

Length between two lenses

=1331 + 470

= 1801 mm

= 1.8 m Ans