With the use of the formula SinФ = nλ / d, there are 16 spectral orders which can be seen when it is illuminated by white light.
Given that a grating has 2000 slits/cm. That is,
d = 0.01 / 2000
d = 5 x
m
The wavelength λ = (700 - 400) nm
λ = 300 x
m
To calculate how many full spectral orders that can be seen (400 to 700 nm) when it is illuminated by white light, we will use the below formula
SinФ = nλ / d
Φ =
(nλ / d)
When n = 1
Φ =
(300 x
/ 5 x
)
Φ = 3.4 degrees
when n = 2
Φ =
(2 x 300 x
/ 5 x
)
Ф = 6.9 degrees
When n = 3
Ф =
(3 x 300 x
/ 5 x
)
When n = 16
Ф =
(16 x 300 x
/ 5 x
)
Ф =
(0.96)
Ф = 73.7 degrees
when n = 17
Ф =
(17 x 300 x
/ 5 x
)
Ф =
(1.05)
Ф = Error ( that is, it does not exist)
Therefore, there are 16 spectral orders which can be seen when it is illuminated by white light.
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Answer:
The ratio of lengths of the two mathematical pendulums is 9:4.
Explanation:
It is given that,
The ratio of periods of two pendulums is 1.5
Let the lengths be L₁ and L₂.
The time period of a simple pendulum is given by :

or

Where
l is length of the pendulum

or
....(1)
ATQ,

Put in equation (1)

So, the ratio of lengths of the two mathematical pendulums is 9:4.
I can't answer this question without a figure. I've found a similar problem as shown in the first picture attached. When adding vectors, you don't have to add the magnitudes only, because vectors also have to factor in the directions. To find the resultant vector C, connect the end tails of the individual vectors.
<em>The red line (second picture) represents the vector C.</em>