Question

An achromatic combination of lenses produce
A. Images in black and white
B. Colored images
C. Images unaffected by variation of refractive index with wavelength
D. Highly enlarged images are formed

Answer 1

Hint: The achromatic lens is free from chromatic aberrations. The wavelength of light is inversely proportional to the refractive index of the medium and the focal length is directly proportional to the wavelength of light used.

Complete step by step answer:
To answer this question we need to understand the definition of achromatic lens combination. Achromatic combination of lenses is the combination of two lenses of different nature and of different focal lengths. We know that the image produced by achromatic combination is free from chromatic aberrations.

We know that focal length of the lens is proportional to the wavelength of light used. The focal length of the combination of two lenses is given as,
\[\dfrac{1}{f} = \dfrac{1}{{{f_1}}} + \dfrac{1}{{{f_2}}}\]

Here, \[{f_1}\] and \[{f_2}\] are the focal lengths of two lenses respectively.

If we combine a convex and concave lens properly, the focal length of the combined lens will not change for different wavelengths of light. This combination of lenses is known as achromatic lens.

We know that the wavelength of light is inversely proportional to the wavelength. Due to achromatic combination of lenses, the image of the object is unaffected by the variation of the refractive index with wavelength.

In the achromatic combination of the lenses, chromatic aberrations of one lens are balanced by the chromatic aberrations of the lens placed next to it. Due to this, the white light does not undergo dispersion. Therefore, the images are not black and white. Thus, the option (A) is incorrect.

So, the correct answer is “Option C”.

Note:
To answer these types of questions, students should know the signs of focal length of convex lens and concave lens. The focal length of a convex lens is positive while the focal length of a convex lens is negative. The dispersion of light also should be known to us. It is the dispersion of white light into its constituent colors while passing through a certain material like prism or water.