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In India, we find mangoes with different...

In India, we find mangoes with different flavours, colours, fibre contents, sugar contents and shelf life. The large variation is due to

A

Genetic diversity

B

Species diversity

C

Induced mutations

D

Hybridisation.

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A
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In India, we find mangoes with different flavours, colours, fibre content , sugar content and even shelf-life. The large variation is on account of

In India, we find mangoes with different flavours, colours, fibre content , sugar content and even shelf-life. The large variation is on account of (a) Species diversity (b) Induced mutations (c) Genetic diversity (d) Hybridisation

In India, there are several types of rice that differ i n grain size, texture, colour and aroma. This is due to

The image of a white object in with light formed by a lens is usually colored and blurred. This defect of image is called chromatic aberration and arises due to the fact that focal length of a lens is different for different colours. As R . I . mu of lens is maximum for violet while minimum for red, violet is focused nearest to the lens while red farthest from it as shown in figure. As a result of this, in case of convergent lens if a screen is placed at F_(v) center of the image will be violet and focused while sides are red and blurred. While at F_(R) , reverse is the case, i.e ., center will be red and focused while sides violet and blurred. The differece between f_(v) and f_(R) is a measure of the longitudinal chromatic aberration (L.C.A),i.e., L.C.A.=f_(R)-f_(v)=-df with df=f_(v)-f_(R) ........... (1) However, as for a single lens, (1)/(f)=(mu-1)[(1)/(R_(1))-(1)/(R_(2))] ............. (2) rArr -(df)/(f^(2))=dmu[(1)/(R_(1))-(1)/(R_(2))] ............... (3) Dividing E1n. (3) by (2) : -(df)/(f)=(dmu)/((mu-1))=omega, [omega=(dmu)/((mu-1))] "dispersive power" , .........(4) And hence, from Eqns. (1) and (4) , L.C.A.=-df=omegaf Now, as for a single lens neither f nor omega zero, we cannot have a single lens free from chromatic aberration. Condition of Achromatism : In case of two thin lenses in contact (1)/(F)=(1)/(F_(1))+(1)/(F_(2)) i.c,. -(dF)/(F^(2))=(df_(1))/(f_(1)^(2))-(df_(2))/(f_(2)^(2)) The combination will be free from chromatic aberration if dF=0 i.e., (df_(1))/(f_(1)^(2))+(df_(2))/(f_(2)^(2))=0 which with the help of Eqn. (4) reduces to (omega_(1)f_(1))/(f_(1)^(2))+(omega_(2)f_(2))/(f_(2)^(2))=0 , i.e., (omega_(1))/(f_(1))+(omega_(2))/(f_(2))=0 ........(5) This condition is called condition of achromatism (for two thin lenses in contact ) and the lens combination which satisfies this condition is called achromatic lems, from this condition, i.e., form Eqn. (5) it is clear the in case of achromatic doublet : Since, if omega_(1)=omega_(2), (1)/(f_(1))+(1)/(f_(2))=0 i.e., (1)/(F)=0 or F=infty i.e., combination will not behave as a lens, but as a plane glass plate. (2) As omega_(1) and omega_(2) are positive quantities, for equation (5) to hold, f_(1) and f_(2) must be of opposite nature, i.e., if one of the lenses is converging the other must be diverging. (3) If the achromatic combination is convergent, f_(C)ltf_(D) and as (f_(C))/(f_(d))=(omega_(C))/(omega_(D)), omega_(C)ltomega_(d) i.e., in a convergent achromatic doublet, convex lens has lesses focal legth and dispersive power than the divergent one. A combination is made of two lenses of focal lengths f and f' in contact , the dispersive powers of the materials of the lenses are omega and omega' . The combination is achromatic when :

The image of a white object in with light formed by a lens is usually colored and blurred. This defect of image is called chromatic aberration and arises due to the fact that focal length of a lens is different for different colours. As R . I . mu of lens is maximum for violet while minimum for red, violet is focused nearest to the lens while red farthest from it as shown in figure. As a result of this, in case of convergent lens if a screen is placed at F_(v) center of the image will be violet and focused while sides are red and blurred. While at F_(R) , reverse is the case, i.e ., center will be red and focused while sides violet and blurred. The differece between f_(v) and f_(R) is a measure of the longitudinal chromatic aberration (L.C.A),i.e., L.C.A.=f_(R)-f_(v)=-df with df=f_(v)-f_(R) ........... (1) However, as for a single lens, (1)/(f)=(mu-1)[(1)/(R_(1))-(1)/(R_(2))] ............. (2) rArr -(df)/(f^(2))=dmu[(1)/(R_(1))-(1)/(R_(2))] ............... (3) Dividing E1n. (3) by (2) : -(df)/(f)=(dmu)/((mu-1))=omega, [omega=(dmu)/((mu-1))] "dispersive power" , .........(4) And hence, from Eqns. (1) and (4) , L.C.A.=-df=omegaf Now, as for a single lens neither f nor omega zero, we cannot have a single lens free from chromatic aberration. Condition of Achromatism : In case of two thin lenses in contact (1)/(F)=(1)/(F_(1))+(1)/(F_(2)) i.c,. -(dF)/(F^(2))=(df_(1))/(f_(1)^(2))-(df_(2))/(f_(2)^(2)) The combination will be free from chromatic aberration if dF=0 i.e., (df_(1))/(f_(1)^(2))+(df_(2))/(f_(2)^(2))=0 which with the help of Eqn. (4) reduces to (omega_(1)f_(1))/(f_(1)^(2))+(omega_(2)f_(2))/(f_(2)^(2))=0 , i.e., (omega_(1))/(f_(1))+(omega_(2))/(f_(2))=0 ........(5) This condition is called condition of achromatism (for two thin lenses in contact ) and the lens combination which satisfies this condition is called achromatic lems, from this condition, i.e., form Eqn. (5) it is clear the in case of achromatic doublet : Since, if omega_(1)=omega_(2), (1)/(f_(1))+(1)/(f_(2))=0 i.e., (1)/(F)=0 or F=infty i.e., combination will not behave as a lens, but as a plane glass plate. (2) As omega_(1) and omega_(2) are positive quantities, for equation (5) to hold, f_(1) and f_(2) must be of opposite nature, i.e., if one of the lenses is converging the other must be diverging. (3) If the achromatic combination is convergent, f_(C)ltf_(D) and as (f_(C))/(f_(d))=(omega_(C))/(omega_(D)), omega_(C)ltomega_(d) i.e., in a convergent achromatic doublet, convex lens has lesses focal legth and dispersive power than the divergent one. Chromatic aberration of a lens can be corrected by :

The image of a white object in with light formed by a lens is usually colored and blurred. This defect of image is called chromatic aberration and arises due to the fact that focal length of a lens is different for different colours. As R . I . mu of lens is maximum for violet while minimum for red, violet is focused nearest to the lens while red farthest from it as shown in figure. As a result of this, in case of convergent lens if a screen is placed at F_(v) center of the image will be violet and focused while sides are red and blurred. While at F_(R) , reverse is the case, i.e ., center will be red and focused while sides violet and blurred. The differece between f_(v) and f_(R) is a measure of the longitudinal chromatic aberration (L.C.A),i.e., L.C.A.=f_(R)-f_(v)=-df with df=f_(v)-f_(R) ........... (1) However, as for a single lens, (1)/(f)=(mu-1)[(1)/(R_(1))-(1)/(R_(2))] ............. (2) rArr -(df)/(f^(2))=dmu[(1)/(R_(1))-(1)/(R_(2))] ............... (3) Dividing E1n. (3) by (2) : -(df)/(f)=(dmu)/((mu-1))=omega, [omega=(dmu)/((mu-1))] "dispersive power" , .........(4) And hence, from Eqns. (1) and (4) , L.C.A.=-df=omegaf Now, as for a single lens neither f nor omega zero, we cannot have a single lens free from chromatic aberration. Condition of Achromatism : In case of two thin lenses in contact (1)/(F)=(1)/(F_(1))+(1)/(F_(2)) i.c,. -(dF)/(F^(2))=(df_(1))/(f_(1)^(2))-(df_(2))/(f_(2)^(2)) The combination will be free from chromatic aberration if dF=0 i.e., (df_(1))/(f_(1)^(2))+(df_(2))/(f_(2)^(2))=0 which with the help of Eqn. (4) reduces to (omega_(1)f_(1))/(f_(1)^(2))+(omega_(2)f_(2))/(f_(2)^(2))=0 , i.e., (omega_(1))/(f_(1))+(omega_(2))/(f_(2))=0 ........(5) This condition is called condition of achromatism (for two thin lenses in contact ) and the lens combination which satisfies this condition is called achromatic lems, from this condition, i.e., form Eqn. (5) it is clear the in case of achromatic doublet : Since, if omega_(1)=omega_(2), (1)/(f_(1))+(1)/(f_(2))=0 i.e., (1)/(F)=0 or F=infty i.e., combination will not behave as a lens, but as a plane glass plate. (2) As omega_(1) and omega_(2) are positive quantities, for equation (5) to hold, f_(1) and f_(2) must be of opposite nature, i.e., if one of the lenses is converging the other must be diverging. (3) If the achromatic combination is convergent, f_(C)ltf_(D) and as (f_(C))/(f_(d))=(omega_(C))/(omega_(D)), omega_(C)ltomega_(d) i.e., in a convergent achromatic doublet, convex lens has lesses focal legth and dispersive power than the divergent one. Chromatic aberration in the formation of image by a lens arises because :

State true or false statements. Correct each false statements to make it true. (i) Within a species, genetic diversity occurs in the differences of alleles, entire genes and chromosomal structures. (ii) 1000 varieties of rice occur in India due to genetic variation. (iii) Ecosystem diversity is high in Norway because of the occurrence of a large number of ecosystems.