Question

two thin lenses having focal length + 20 cm and - 30 cm are put in contact the doublet behave as an achromatic lens find the focal length of this doublet what will the converging power of the focal length of the two lenses made the same?

Answer 1

HI,

Two key facts:

The power of a lens is the reciprocal of the focal length in meters.

Powers are additive.

The lens with a focal length of +20 cm has a power of 1/0.2 = +5.

The lens with a focal length of -15 cm has a power of 1/(-0.15 ) = -6.67

The two lenses together have a power of 5 - 6.67 = -1.67.

The focal length of the combination is 1/(-1.67) = -0.6 or -60 cm.

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Answer 2

Answer:

The Focal length of this doublet is $60 \ cm$ A concave lens has a negative focal length. Therefore, it is a concave lens.

Explanation:

• The achromatic lens is composed of convex and concave lenses made of two glasses with different optical properties. Coronal glass with a small refractive index and large dispersion ability is often used to make a convex lens, and flint glass with a large refractive index and small dispersion ability is used to make the concave lens.
• Generally, the difference lens can only overlap the image points of the two main color lights, to eliminate the color difference of the two-color lights.

Two key facts:

• The power of a lens is the reciprocal of the focal length in meters.
• Powers are additive.
• The lens with a focal length of +20 cm has a power of $\frac{1}{0.2} = +5.$

The lens with a focal length of -30 cm has a power of$\frac{1}{-0.30} = -3.33$

The two lenses together have a power of $5 - 3.33 = 1.67.$

The focal length of the combination is $\frac{1}{1.67}=0.59880 \\=0.6 \ or \ 60 \ cm$

A concave lens has a negative focal length. Therefore, it is a concave lens.