This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: "https://hubpages.com/privacy-policy#gdpr"

Show Details
Necessary
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
Features
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Marketing
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Statistics
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
jump to last post 1-3 of 3 discussions (7 posts)

When you "cross" (90 degrees) two high-quality polarizing lenses, what happens?

  1. Laura Schneider profile image92
    Laura Schneiderposted 5 years ago

    When you "cross" (90 degrees) two high-quality polarizing lenses, what happens?

    Now, what happens when you put a third polarizing lens between the first two at a random (but unequal) angle with respect to the first to lenses? And can you explain why?

  2. Larry Fields profile image76
    Larry Fieldsposted 5 years ago

    With the first two lenses, you'd filter out essentially all of the incoming light. Adding the intermediate third lens would allow some of the light to pass through. Sorry; I can visualize it, but I can't explain it.

    1. Laura Schneider profile image92
      Laura Schneiderposted 5 years agoin reply to this

      Ding ding ding! You are correct, Sir! I'm pleased that someone else was awake during physics class, too.

      The last part of the question, how and why it works that way, we'll leave to someone else: you've gotten us off the ground.

      Anyone? Guesses?

  3. profile image0
    calculus-geometryposted 5 years ago

    The explanation of the paradox is due to the fact that polarizing lenses don't "filter" in the normal sense of the word, they reduce the strength of light that passes through according to the angle of the light source and the angle of orientation of the lens.

    To illustrate, suppose the first two lenses are at angles of 0 degrees and 90 degrees, and that the middle lens is oriented at x degrees with x between 0 and 90.

    In the two-lens case, when light at an angle of z passes through the first lens (0 degrees, horizontal) the vertical component of the light is flattened. When that now horizontal light passes through the second lens (90 degrees, vertical) the horizontal component of the light is flattened and only the magnitude of the vertical component matters.  But at this point, after having passed through the first lens, there is no vertical component, therefore the magnitude of the output light is 0, no light at all.

    In the three-lens case, when the light passes through the lens oriented 0 degress and then the lens oriented x degrees (in the middle), the intensity of the light reduces to cos(x) of its original intensity. After it passes through the middle lens, the light still has some horizontal and vertical component.  Finally, when it passes through the last lens (90 degrees) the intensity is reduced by sin(x).  So the net reduction in strength is cos(x)*sin(x). 

    If you choose x = 45 degrees for the middle lens, then the reduction is cos(45)*sin(45) = 0.5.  So the light is reduced to 50% of its original strength.

    1. Laura Schneider profile image92
      Laura Schneiderposted 5 years agoin reply to this

      Excellent proof! You must be a professor, genius, over-educated unit of the general public, or all of these. :-)  Larry's answer got us off to a great start, and yours fleshed out the details. Congrats and thanks! I selected this as the Best Answer!

    2. SidKemp profile image93
      SidKempposted 5 years agoin reply to this

      Fascinating - I did not know abut the effect of adding the third lens. This means that the light leaving the 1st lens has its horizontal component eliminated at the lens, but it is somewhat restored before it reaches the intermediate lens,  I think.

    3. Laura Schneider profile image92
      Laura Schneiderposted 5 years agoin reply to this

      SidKemp--It boggles the mind, doesn't it? The 3rd, odd-angled filter introduces a perpendicular component back in to the mix because photons are not just waves or just particles, but rather hybrids of both: waveicles. Cool!

 
working