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Murrr4er [49]
3 years ago
9

The smallest known galaxy, Segue 2, has an approximate radius of 1.05 × 1015 kilometers. Use the conversion factors 1 light-year

= 9.5 × 1012 kilometers and 1 parsec = 3.262 light-years to convert this distance from kilometers to parsecs. Choose the closest answer.
Physics
1 answer:
scoundrel [369]3 years ago
5 0

( 1.05 x 10¹⁵ km ) x ( 1 LY / 9.5 x 10¹² km ) x ( 1 psc / 3.262 LY ) =

(1.05) / (9.5 x 3.262) x (km · LY · psc) / (km · LY) x (10¹⁵⁻¹²) =

(0.03388) x (psc) x (10³) =

33.88 parsecs


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t = 905.8 nm

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Given:

- Wavelength λ_1 = 500 nm

- Wavelength λ_2 = 625 nm

- MgF₂ refractive index n = 1.38

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What is the thinnest film for which this can occur?

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- We have two different wavelength of light that constructively interfere at the surface of the film. We need the minimum thickness of film that would satisfy the condition of constructive interference for both!

-Since the refractive index of glass is greater than that of MgF_2, the expression of constructive interference would be as follows:

                                2*t = m*λ / n

- Since, the orders m are unknown for each wavelength, also different. We will try to determine the first for each wavelength of light.

- Construct two equation:

                                t = m_1*(500 nm ) / (2*1.38 )

                                t = 181.1594203*m_1  nm

                                t = m_2*(625 nm ) / (2*1.38 )

                                t = 226.4492754*m_2  nm

- Now equate the two thicknesses which should be equal:

                               226.4492754*m_2 = 181.1594203*m_1

                               m_2 = 0.8*m_1

- Now we know that m can only take integer values, and m is proportional to thickness t. So for thinnest thickness m's must take the least integer values. Hence, we have:                    

                               m_2 = (4 / 5) * m_1

So,                           m_1 = 5 , m_2 = 4   ..... Least integer values.

- Now that we have m's we can compute the thickness t as follows:

                                t = 181.1594203*m_1  nm

- Substitute m_1 = 5, we have:

                                t = 181.1594203*5  nm

                               t = 905.8 nm

- Substitute m_2 = 4 in:

                                 t = 226.4492754*m_2

                                 t = 226.4492754*4

                                t = 905.8 nm

- Our values of t = 905.8 nm matches for both wavelengths.

                                   

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