The Least Time Principle Interactive is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Interactive can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

Teaching Ideas and Suggestions:

This Interactive is intended for use near the early to middle stages of a learning cycle on Snell's law. We suggest that it be used after some practical lab work that leads to the derivation of Snell's law using experimental data.
Users are encouraged to open the Interactive and explore. If desired, a prepared activity created by The Physics Classroom could be used for a more directed experience. The activity is designed to be used by a class of students. Each lab group is assigned a set of speeds with the challenge of determining the entry point that leads to the least time. Once found, the angles of incidence and reflection are measured and shared with the class as a whole. With several lab groups particpating, a collection of data leading  to the conclusion that the ratio of the sines of the angles is inversely related to the ratio of the speeds in each respective medium. This relatioinship can be used along the n = c/v equation to derive Snell's law from the Principle of Least Time.While emperical evidence is the basis for believing in Snell's law, the principle of least time is the underlying basis for why such a law exists. Vist the Activity Page to access and print the Activity directions.

Related Resources

There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Least Time Principle Interactive. These include:
  • Minds On Physics Internet Modules:
    The Minds On Physics Internet Modules include a collection of interactive questioning modules that help learners assess their understanding of physics concepts and solidify those understandings by answering questions that require higher-order thinking. Assignments RL1, RL2, RL3, and RL5 of the Refraction and Lenses module provide great complements to this Interactive. They are best used in the middle to later stages of the learning cycle. Visit the Minds On Physics Internet Modules.
  • Curriculum/Practice: Several Concept Development worksheets at the Curriculum Corner will be very useful in assisting students in cultivating their understanding, most notably ...

    Light Refraction
    Direction of Bending
    Snell's Law
    Total Internal Reflection

    Visit the Curriculum Corner.
  • Labwork: 
    Simulations should always support (never supplant) hands-on learning. The Laboratory section of The Physics Classroom website includes several hands-on ideas that complement this Interactive. Five notable lab ideas include ...

    Refraction Action
    Direction of Bending
    How Much? Lab
    The Unknown n Lab
    R and R Lab

    Visit The Laboratory.
  • Science Reasoning Activities:
    Science classrooms should be filled with reasoning activities. There are two related activities in the Refraction section of the Science Reasoning Center that will challenge students to employ close reading, data analysis, and logical reasoning. The activities are named ...

    Snell's Law
    Reflection and Transmission

    Visit the Science Reasoning Center.

Additional resources and ideas for incorporating the Least Time Principle into an instructional unit on refraction can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.


The Physics Classroom would like to extend a special thanks to Nerd Island Studios for the creation of this HTML5 Interactive. Visit to see more great stuff by Nerd Island Studios.

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