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What are the two focal length of a lens? Are they equal?

Important Questions on Refraction of Light at Spherical Surfaces : Lenses

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12th ICSE
IMPORTANT
ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 10
The image of a candle is formed by a convex lens on a screen. If the lower half of the lens is painted black to make it completely opaque, will still the full-size image of the candle be obtained?
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ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 11
What will be the effect on focal length and nature of a lens when immersed in a liquid whose refractive index is less than that of the material of the lens?
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ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 12
A concave mirror and a concave lens are held in water. What changes, if any, do you expect in their focal lengths as compared to their values in air?
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ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 13
Can a convex (converging) lens behave as a concave (diverging) lens in some situation? Give example.
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12th ICSE
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ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 14
A convex lens forms the image of the sun at a distance of 10 cm. Where will the image be formed, if a lens of the same power but of double the aperture is used?
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12th ICSE
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ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 14
A convex lens forms the image of the sun at a distance of 10 cm. Where will the image be formed, if a lens of the same aperture but of double the power is used?
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ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 15

In the figure shown, O is a point object placed in the air on the axis of a spherical surface APB of a glass block. OA is an incident ray. The direction of the refracted ray AD in the glass block is parallel to the principal axis PC. CP=CA=R is the radius of the spherical surface. Use the formula n2v−n1u=n2−n1R to show that the object distance PO=u=R(n−1); where n2=n and n1=1.

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12th ICSE
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ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 16
A monochromatic ray of light is incident on a spherical refracting surface of refractive index n. If f1 and f2 be the first and second focal lengths of the surface, show that f2+nf1=0.