Find Glass Thickness to Block 25% of Light in Sunglasses

In summary, the intensity of light passing through a pair of sunglasses is given by the equation I(x) = I0 (0.8)^x, where x is the thickness of the glass in millimeters and I0 is the intensity of light entering the glasses. To block 25% of the light entering the sunglasses, the thickness of the glass should be such that 0.75 times the initial intensity (I0) is equal to I0 (0.8)^x. This can be solved by using logarithms and exponentials to find the value of x.
  • #1
fxacx
4
0
The intensity, I of light in lumens, passing through the glass of a pair of sunglasses is given by the
equation I(x) = I0 (0.8)^x , where x is the thickness of the glass in millimetres and I0 is the intensity of
light entering the glasses. How thick should the glass be so that it will block 25% of the light entering
the sunglasses?
 
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  • #2
H
fxacx said:
The intensity, I of light in lumens, passing through the glass of a pair of sunglasses is given by the
equation I(x) = I0 (0.8)^x , where x is the thickness of the glass in millimetres and I0 is the intensity of
light entering the glasses. How thick should the glass be so that it will block 25% of the light entering
the sunglasses?

$0.75 I_0 = I_0 (0.8)^x$

solve for x ...
 
  • #3
So the question is, again, do you know how to solve $a^x= y$? You titled this "Log/exponential word problem". Do you know what "logarithms" and "exponentials" are and how they are related?
 

1. How do you determine the thickness of glass needed to block 25% of light in sunglasses?

The thickness of glass needed to block 25% of light in sunglasses can be determined using the Beer-Lambert Law, which states that the amount of light absorbed by a material is directly proportional to its thickness. By knowing the initial intensity of light and the desired intensity after passing through the glass, the thickness can be calculated using this formula: t = -ln(T)/μ, where t is the thickness, T is the desired transmittance (in this case, 0.25), and μ is the absorption coefficient of the glass.

2. What factors affect the thickness of glass needed to block 25% of light in sunglasses?

The main factors that affect the thickness of glass needed to block 25% of light in sunglasses are the initial intensity of light, the desired intensity after passing through the glass, and the absorption coefficient of the glass. Other factors that may also play a role include the type and quality of the glass, as well as the angle at which the light passes through the glass.

3. Can the thickness of glass vary for different types of sunglasses?

Yes, the thickness of glass needed to block 25% of light in sunglasses can vary depending on the type and quality of the sunglasses. For example, sunglasses with polarized lenses may require a different thickness of glass compared to non-polarized sunglasses to achieve the same level of light blocking. Additionally, different materials used for the lenses, such as plastic or polycarbonate, may also require different thicknesses of glass to achieve the desired level of light blocking.

4. Is there an ideal thickness of glass for sunglasses to block 25% of light?

There is no one ideal thickness of glass for sunglasses to block 25% of light, as it depends on various factors such as the type of sunglasses, the material of the lenses, and the desired level of light blocking. However, it is important to ensure that the glass is not too thin, as it may not effectively block 25% of light, and not too thick, as it may make the sunglasses heavy and uncomfortable to wear.

5. Are there any other methods for achieving 25% light blocking in sunglasses besides using glass?

Yes, there are other methods for achieving 25% light blocking in sunglasses besides using glass. Some sunglasses may use tinted plastic lenses or coatings to block 25% of light. However, the thickness of these materials may vary and may not follow the same formula as glass. It is important to check the specifications of the sunglasses to ensure that they meet the desired level of light blocking.

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