Optical sheet, backlight and liquid crystal display apparatus

A backlight comprising:

• a light source for emitting illumination light;
• and
• an optical sheet for raising a directivity of a illumination light emitted from said light source;
• said optical sheet has, provided on one of principal faces thereof, cylindrical lens elements which have a hyperboloidal face or a paraboloidal face and are provided successively in a row;
• where a Z axis is taken in parallel to a normal line direction to said optical sheet and an X axis is taken in a direction of the row of said cylindrical lens elements, a cross sectional shape of said cylindrical lenses satisfies the following expression:
• Z=X2/(R+√{square root over ( )}(R2−(1+K)X2))
• where R is the radius of curvature of a distal end vertex, and K is a conic constant.

A liquid crystal display apparatus, comprising:

• a light source for emitting illumination light;
• an optical sheet for raising the directivity of a illumination light emitted from said backlight;
• and
• a liquid crystal panel for displaying an image based on the illumination light emitted from said optical sheet;
• said optical sheet has, provided on one of principal faces thereof, cylindrical lens elements which have a hyperboloidal face or a paraboloidal face and are provided successively in a row;
• where a Z axis is taken in parallel to a normal line direction to said optical sheet and an X axis is taken in a direction of the row of said cylindrical lens elements, a cross sectional shape of said cylindrical lenses satisfies the following expression:
• Z=X2/(R+√{square root over ( )}(R2−(1+K)X2))
• where R is the radius of curvature of a distal end vertex, and K is a conic constant.