Does the Focal Length of a Lens Change When You Move It To A different Sensor Size?

Short Answer:

No.

Long Answer:

What is Focal Length?

Focal Length does not describe the angle of view you get with a lens. Focal Length is a physical property of the lens, and does not change if the lens is moved to a body with a different sensor size.

Roughly speaking, the focal length of a simple lens is how far the lens should be from the sensor, in order for objects that are very far away to be in focus.

"Angle of View" is how wide (or narrow) a view you are getting from the camera. Often it is measured in degrees across the diagonal of the frame. The primary factors in Angle of View are the focal length of the lens, and the sensor size.

For instance, a 50mm lens on a full frame camera yields about a 46° Angle of View. That same 50mm lens on a 2X crop body would yield about a 23° Angle of View. Same lens, same focal length, different Angles of View.

A 25mm lens mounted on a 2X body also yields a 46° Angle of View. Yet, it is still a 25mm lens.

A Confusing Choice of Units

A lot of confusion arises because many camera manufacturers don't like using degrees to describe Angle of View.

A lot of companies describe Angle of View in units of "Focal Length that would be needed on a traditional 35mm film SLR"

This is often shortened to "Equivalent Focal Length" or "Effective Focal Length."

A 50mm lens on a traditional 35mm film SLR camera yields a 46° angle of view. Therefore any body/lens combination that yields a 46° Angle of View might be called "50mm Equivalent Focal Length". So a 25mm lens on a 2X crop body yields a "50mm equivalent focal length Angle of View".

It's important to remember that "Focal Length" is describing a physical property of the lens. "Equivalent Focal Length" is describing the resulting Angle of View. Note that "Focal Length" and "Equivalent Focal Length" are describing different things.

Put a 25mm lens on a full frame camera and it is a 25mm Focal Length lens yielding a 25mm Equivalent Focal Length Angle of View (82°). Put that same lens on a 2X crop body, and it is still a 25mm Focal Length lens, but it now yields a 50mm Equivalent Focal Length Angle of View (46°).