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The index of refraction of a glass varies with the wavelength of the light passing through it. This has important consequences for the design of optical instruments. A type of glass known as "extra-dense flint" has an n = 1.7378 for blue light, and an n of 1.7130 for red light. Calculate the focal length of the lens above, for both red and blue light.

As just been pointed out to me the Lens must be from the question before it which is:

The so-called "lensmakers equation" is shown below. The focal length of the lens (in cm) is f. The constant n is the index of refraction of the glass, relative to the medium around it (which is just the listed value of n unless the lens is submerged in water, or some other liquid). R1 and R2 are the radii of curvature of the two sides of the lens. The value of R for a side is considered to be positive if that side is convex; otherwise, it is negative. If the lens is flat on one side, the value of R for that side is infinite, and the ratio (1/R) is equal to zero.

1/f=(n-1)(1/R_1 + 1/R_2 )


Assume the lens is biconvex; that is, that both sides are convex. The radii of curvature are both 30 cm. The coefficient of refraction is 1.60. What is the focal length of the lens, in cm?

The answer for this was given as:

1/f=(n-1)(1/R1 + 1/R2 )

=> 1/f=(1.6-1)(1/30 + 1/30 )

=>1/f= 0.6(1/15 )

=> f= 15/.6 = 25 cm

Explanation / Answer

See if you know the lens maker formula all you need to do is put the value in it and calculate the Focal length. In you question you have two "n" so you will have to solve it twice. But R is missing from the question.
1/f=(n-1)(1/R1 + 1/R2 )
so if You know the value of R1 and R2 just put it in the formula with both the n's one by one and solve.

So if the R1 = R2 =30

Case 1 Blue Light: n =  n = 1.7378

1/f=(n-1)(1/R1 + 1/R2 ) = 1/f=(1.7378-1)(1/30 + 1/30 ) => 1/f=0.7378*2/30 => f=  20.33

Case 2 Red Light: n =  1.7130

1/f=(n-1)(1/R1 + 1/R2 ) = 1/f=(1.7130-1)(1/30 + 1/30 ) => 1/f=0.7130*2/30 => f= 21.037

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