Question

A sunscreen blocks \(95 \%\) of the sun's harmful UV rays. What is the sunscreen's SPF?

Short answer

The sunscreen's SPF is 20.

Step-by-step solution

Understand the Relationship

SPF (Sun Protection Factor) indicates how much longer someone can stay in the sun without getting sunburned when using the sunscreen. The SPF rating is connected to the percentage of UV rays blocked.

Calculate the Remaining UV Exposure

Since the sunscreen blocks 95% of the UV rays, only 5% of the UV rays can penetrate the sunscreen. In decimal form, 5% is represented as 0.05.

Determine the SPF Value

The formula for SPF is the reciprocal of the unblocked fraction of UV rays: \[ \text{SPF} = \frac{1}{\text{unblocked fraction}} \] Plugging in the value, we get \[ \text{SPF} = \frac{1}{0.05} = 20 \]

Key concepts

Sunscreen

Sunscreen is a product applied to the skin to protect it from the harmful effects of the sun's ultraviolet (UV) rays.
It's available in many forms, including lotions, sprays, and gels.
Sunscreens contain ingredients that either absorb, reflect, or scatter UV radiation.
Using sunscreen helps prevent sunburn, premature skin aging, and even skin cancer.
The effectiveness of a sunscreen is often measured by its Sun Protection Factor (SPF).
The higher the SPF, the more protection it offers.

UV rays

UV rays are part of the invisible light spectrum emitted by the sun.
They are classified into three types: UVA, UVB, and UVC.
UVA rays can age skin and cause long-term skin damage.
UVB rays are more intense and are the main cause of sunburns.
UVC rays are absorbed by the Earth's atmosphere and do not reach the ground.
Exposure to these rays can damage skin cells, leading to various skin problems.
Sunscreens with broad-spectrum protection shield you from both UVA and UVB rays.

Percentages

Percentages are a way to express a portion of a whole out of 100.
For example, 95% means 95 out of every 100 parts.
In the context of sunscreen, a sunscreen that blocks 95% of UV rays lets only 5% through.
This remaining 5% can be converted to a decimal (0.05) for calculations.
Understanding percentages helps in determining how effective a sunscreen is in blocking harmful UV rays.

Reciprocal

A reciprocal is simply 1 divided by a number.
In the SPF calculation, the reciprocal of the unblocked fraction of UV rays is used.
If a sunscreen blocks 95% of UV rays, 5% are not blocked.
The fraction of unblocked rays (5%) in decimal form is 0.05.
The reciprocal of 0.05 is calculated as \(\frac{1}{0.05}\).
The result of this calculation gives us the SPF value.
In this example, the SPF is 20, meaning you can stay in the sun 20 times longer without getting sunburned.