Question

If the wavelength of light is \(4000^{\circ} \mathrm{A}\) then the number of waves in \(1 \mathrm{~mm}\) length will be (A) \(2.5\) (B) 2500 (C) 250 (D) 25000

Short answer

The number of waves in 1 mm length, given the wavelength of light is \(4000^{\circ} \mathrm{A}\), is 25000.

Step-by-step solution

Convert the given units into millimeters

First, we need to convert the given wavelength (in Angstroms) into millimeters. We know that \(1 \mathrm{~A} = 10^{-10} \mathrm{~m}\) and \(1 \mathrm{~mm} = 10^{-3} \mathrm{~m}\). Therefore, to convert Angstroms to millimeters, we can use the following formula: Wavelength (in mm) = Wavelength (in A) × \(10^{-10} \mathrm{~m}\) / \(10^{-3} \mathrm{~m}\) For the given wavelength of \(4000^{\circ} \mathrm{A}\): Wavelength (in mm) = \(4000 \times (10^{-10} / 10^{-3}) = 4000 \times 10^{-7}\) Now, we have the wavelength in mm.

Calculate the number of waves

To find the number of waves in 1 mm length, we can use the formula: Number of waves (N) = Length / Wavelength In this case, the Length is 1 mm, and we have already calculated the Wavelength in step 1. Hence, N = 1 mm / (4000 x \(10^{-7}\) mm) N = \(1 / (4000 \times 10^{-7})\) N = \(10^{7} / 4000\) N = 25000

Choose the correct answer

The number of waves in 1mm length is 25000. Therefore, the correct answer is: (D) 25000